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<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>Triangle $XYZ$ is such that&nbsp;$XY=15.8$ cm, $YZ=28.4$ cm and $\angle YXZ=74{}^\circ $.<br>Calculate</p><ol class="i-list"><li><div class="list-item-paragraph">$\angle XZY$,</div></li><li><div class="list-item-paragraph">the area of$\Delta XYZ$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767358482898-4nvsz8edjqg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTg0ODI4OTgtNG52c3o4ZWRqcWcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.mtFk254dkYaOsVqSG5raYw3kXA1Hgao0JrrTIZtIOYA" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Sine Rule

Non-Right Angled Trigonometry: The Sine Rule for Area

Trigonometry

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>In triangle $XYZ$, $XY=15.8$ cm, $YZ=28.4$ cm and $\angle YXZ=74{}^\circ $.</p><ol class="i-list"><li><div class="list-item-paragraph">Calculate $\angle XZY$.</div></li><li><div class="list-item-paragraph">Calculate the area of $\Delta XYZ$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767357909216-y7ja1zu7ffl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTc5MDkyMTYteTdqYTF6dTdmZmwucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.Pv4QzFOkDyn_HjCzjSyDyM1CteEgJvuTw6uy1VWjanY" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Applying Sine Rule When Given 2 Sides and 1 Non-Included Angle

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>In the diagram, angle $ABC=35{}^\circ $, angle $CAB=62{}^\circ $ and length of $BC=21$ cm.<br>Calculate</p><ol class="i-list"><li><div class="list-item-paragraph">the length of $AC$,</div></li><li><div class="list-item-paragraph">the area of triangle $ABC$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767357745026-6d0h32c2n07.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTc3NDUwMjYtNmQwaDMyYzJuMDcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.KRtAU11u9rSnz6EjWbhjOKuP51xiy4ZGht1Yex2K6F0" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Applying Sine Rule When Given 2 Angles and 1 Side

<p>In the diagram, $\angle BAC=54{}^\circ $, $AB=4.2$ cm, $AC=3.6$ cm, $CD=5.5$ cm and $AD=8$ cm.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Calculate</p><ol class="i-list"><li><div class="list-item-paragraph">the area of $\Delta ABC$, correct to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$\angle ACD$, correct to $1$ decimal place.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767409263479-z9vcqjz0nd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0MDkyNjM0Nzktejl2Y3FqejBuZC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzg5NjEzMDAwLCJleHAiOjE3ODk2MTMzMDB9.tD2tDXBcnvJon9q-4nQ8nCsYIxZnQ631kMKQOzRzkPY" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the diagram, $\angle BAC=54{}^\circ $, $AB=4.2$ cm, $AC=3.6$ cm, $CD=5.5$ cm and $AD=8$ cm.

Cosine Rule

Advanced Euclidean Geometry: The Cosine Rule Challenge

<p>In the diagram, $PCBQ$ is a straight line.  $AB=15$ cm, $\sin \ \angle ABC=\frac{1}{2}$ and $\sin \ \angle ACP=\frac{1}{3}$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">Write down the value of $\sin \ \angle ACB$.</div></li><li><div class="list-item-paragraph">Calculate the length of $AC$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767358747455-wd5ygwibcc.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTg3NDc0NTUtd2Q1eWd3aWJjYy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzg5NjEzMDAwLCJleHAiOjE3ODk2MTMzMDB9.1BOzbAZXkmL3fBmeBXkMFz8ac_Tlni1SnCGmhUjXdpQ" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

In the diagram, $PCBQ$ is a straight line.  $AB=15$ cm, $\sin \ \angle ABC=\frac{1}{2}$ and $\sin \ \angle ACP=\frac{1}{3}$.

Principles of Plane Geometry: Triangle Properties and Proofs

<p>In the diagram, $PRS$ is a straight line, $PQ=12$ cm, $PR=7$ cm and $\sin \angle QRS=\frac{4}{9}$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Calculate the value of</p><ol class="i-list"><li><div class="list-item-paragraph">$\sin \angle PRQ$,</div></li><li><div class="list-item-paragraph">$\sin \angle PQR$, </div></li></ol><p>giving your answers as a fraction in its lowest term.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767358910455-325hiiod3nu.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTg5MTA0NTUtMzI1aGlpb2QzbnUucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.aWZxRnQCTF-X2pRdrmxa2Wja2f9weDjEHJ57aLs4U4Q" style="max-width: min(300px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the diagram, $PRS$ is a straight line, $PQ=12$ cm, $PR=7$ cm and $\sin \angle QRS=\frac{4}{9}$.

Calculating Sine Values in Scalene Triangles

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>In the diagram, triangle $ABC$ is a right-angled triangle where&nbsp;$\angle BAC=90{}^\circ $.</p><ol class="i-list"><li><div class="list-item-paragraph">Find the length of $BC$.</div></li><li><div class="list-item-paragraph">Hence, find the area of triangle $BCD$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767356306094-7ypfl81sftk.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTYzMDYwOTQtN3lwZmw4MXNmdGsucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.-ychgeWI2Dl_WeAI5_E_GrGh5FiSZ8ZLH1NomBSx_j8" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Area of Triangle

Principles of Plane Trigonometry: Area, Sides, and Angles

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>In the diagram, $AB=2x$ cm, $BC=3x$ cm and $AC=4x$ cm.<br>Given that the area of $\Delta ABC$ is $12\sqrt{15}$ cm${}^2$, calculate the value of $x$.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767409031527-gqqzsbyh20c.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0MDkwMzE1MjctZ3FxenNieWgyMGMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.twI9q-vq8fSSMqbtGgmYa3blDS_AzR8zwyoDuMlY4EQ" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Deducing Side Lengths via the Law of Cosines

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The following diagram shows triangle $ABC$ in which the length of $AB$ is $10.2$ cm and the length of $BC$ is $x$ cm.</p><p>Angle $ABC=36{}^\circ $ </p><p>It is given that triangle $ABC$ has an area of $65$ cm$^{2}$, find the value of $x$.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767356512920-y8yhsjl6apg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTY1MTI5MjAteTh5aHNqbDZhcGcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.TqHE-KCBI0ocjDMJPyHosRwTckXY63lyGy5VrthqcJE" style="max-width: min(300px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Analytical Geometry: Bridging Triangle Properties and Algebraic Ratios

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>In $\Delta PQR$, $PQ=5$ cm, $PR=6.5$ cm and $QR=\sqrt{x}$ cm.<br>Given that&nbsp;$\cos \angle QPR = -\frac{11}{52}$, find the value of $x$.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767408808386-zdtky6pheld.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0MDg4MDgzODYtemR0a3k2cGhlbGQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.s4IOSGtd6X5zKKYA3ua1aL8iK6Bwm31tannxeIstRBE" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Trigonometric Analysis of Non-Right Angled Triangles

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The following diagram shows triangle $ABC$ in which the length of $AB$ is $7.5$ cm and the length of $AC$ is $5$ cm.<br>It is given that triangle $ABC$ has an area of $18$ cm$^{2}$, find the obtuse angle $BAC$.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767356057548-o6ppsy7sxi.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTYwNTc1NDgtbzZwcHN5N3N4aS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzg5NjEzMDAwLCJleHAiOjE3ODk2MTMzMDB9.uCYTWXMDKBAsC6Wlj0VdRGirVP4u2SRYUje7UFqiBFg" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>
<p></p>

Solving Inverse Trigonometric Equations to One Decimal Place

<p>In the diagram, $PQ=4$ cm, $QR=6$ cm, $\angle QSR=55{}^\circ$ and $\angle RQS=60{}^\circ$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>Find</p><ol class="i-list"><li><div class="list-item-paragraph">the length of $PR$, correct to $3$ significant figures,</div></li><li><div class="list-item-paragraph">the area of $\Delta QRS$, correct to $3$ significant figures.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767419552325-v2lbg9er3rg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0MTk1NTIzMjUtdjJsYmc5ZXIzcmcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.vkJWPJTyxZqc_jFWqd-TpiboOxSe5X-gHamLUdOqyPI" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the diagram, $PQ=4$ cm, $QR=6$ cm, $\angle QSR=55{}^\circ$ and $\angle RQS=60{}^\circ$.

Determining Geometric Variables using Cosine Ratios

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>In the diagram, $\angle ACB=45{}^\circ $, $\angle CBA=60{}^\circ $ and $AC=100$ m.<br>Calculate</p><ol class="i-list"><li><div class="list-item-paragraph">the length of $BC$,</div></li><li><div class="list-item-paragraph">the area of $\Delta ABC$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767358267096-qkuxn1u5cs.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTgyNjcwOTYtcWt1eG4xdTVjcy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzg5NjEzMDAwLCJleHAiOjE3ODk2MTMzMDB9.3GCqoljDanBs28a4_uVpobT6HfXLfDfun3Hw_PQ3cSI" style="max-width: min(400px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Calculating Triangle Area Using the Sine Rule

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>Calculate the area of triangle $PQR$ where&nbsp;$PQ=30$ m, $QR=40$ m and angle $PQR=60{}^\circ $.</p></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767355821287-ahqaw5a43xl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjczNTU4MjEyODctYWhxYXc1YTQzeGwucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.zno-3NSqJckY6T4wDxlaEZ5eCZAUnq48l7yo6U_rT0I" style="max-width: min(200px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Geometric Analysis of Right-Angled and Extended Triangles

<p>Find the largest angle of a triangle with sides $9$ cm, $12$ cm and $17$ cm.</p>

Find the largest angle of a triangle with sides $9$ cm, $12$ cm and $17$ cm.

Applications of the Cosine Rule in Plane Geometry

<p>In the diagram, $BCD$ is a straight line, $BC=6$ cm, $AC=7.9$ cm, $AD=6.4$ cm and $\angle ACB=130{}^\circ$.<br>Calculate</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="i-list"><li><div class="list-item-paragraph">$AB$,</div></li><li><div class="list-item-paragraph">area of triangle $ABC$,</div></li><li><div class="list-item-paragraph">the shortest distance from $B$ to $AC$ produced,</div></li><li><div class="list-item-paragraph">the obtuse angle $\angle ADC$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767418893671-x35remqpl18.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0MTg4OTM2NzEteDM1cmVtcXBsMTgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc4OTYxMzAwMCwiZXhwIjoxNzg5NjEzMzAwfQ.7JCw6MQWo_C4GLQDZQS1BtWzTBa3ku_bg5FxwsMHG6k" style="max-width: min(300px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

In the diagram, $BCD$ is a straight line, $BC=6$ cm, $AC=7.9$ cm, $AD=6.4$ cm and $\angle ACB=130{}^\circ$.
Calculate

The Relationship Between Side Lengths and Interior Cosines

<p>Find the area of triangle $ABC$ where&nbsp;$AB=6$ cm, $AC=4$ cm and $\angle BAC=19{}^\circ $.</p>
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Find the area of triangle $ABC$ where $AB=6$ cm, $AC=4$ cm and $\angle BAC=19{}^\circ $.

Area Determination for Non-Right-Angled Triangles

<p>In triangle $ABC$, the length of $BC=14$ cm, the length of $AC=16$ cm and angle $BAC=45{}^\circ $.</p>
<p>Find the possible angles of $ABC$.</p>

In triangle $ABC$, the length of $BC=14$ cm, the length of $AC=16$ cm and angle $BAC=45{}^\circ $.

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