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PSLE Foundation Mathematics

<p>A warehouse is $18\text{ m}$ long and $12\text{ m}$ wide, with vertical walls $6\text{ m}$ high.</p>
<div class="graph-block" data-graph-config="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" data-width="500" data-height="330" style="width:500px;height:330px;max-width:100%;display:block;margin:0 auto;"></div>
<p>Its symmetric pitched roof has sloping edges $7.5\text{ m}$ long in each end cross-section. The ridge is directly above the centre line of the warehouse.</p>
<p>Give non-exact numerical answers correct to $3$ significant figures.</p>
<ol class="abc-list"><li data-list-item-id="emath-aot-q11-q-a" data-list-item-path="emath-aot-q11-q-a"><div class="list-item-paragraph">Find the vertical height of the roof ridge above the ground.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="emath-aot-q11-q-b" data-list-item-path="emath-aot-q11-q-b"><div class="list-item-paragraph">Find the distance from a bottom corner to the opposite top corner of the vertical walls.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="emath-aot-q11-q-c" data-list-item-path="emath-aot-q11-q-c"><div class="list-item-paragraph">From the same bottom corner, find the angle of elevation of the ridge point at the opposite end.<span class="inline-marks">[3]</span></div></li></ol>

A warehouse is $18\text{ m}$ long and $12\text{ m}$ wide, with vertical walls $6\text{ m}$ high.

Its symmetric pitched roof has sloping edges $7.5\text{ m}$ long in each end cross-section. The ridge is directly above the centre line of the warehouse.

Give non-exact numerical answers correct to $3$ significant figures.

Trigonometry in Two and Three Dimensions

Angles of Elevation and Depression

Warehouse crane beneath a roof

Trigonometry

<p>The diagram shows a prism whose cross-section area is a right-angled triangle.</p>
<p>$AB=24$ cm, $BC=8$ cm and $FC=6$ cm.</p>
<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/1767444001513-nwkdc5lfac.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0NDQwMDE1MTMtbndrZGM1bGZhYy5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTA0NzgxLCJleHAiOjE3OTM1MDUwODF9.tv20RfPmdwNrpDa0OHP8LsybU6nlNgCzOZoDrFg6IiI" style="max-width: min(250px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<p>Calculate</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the length of $FB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the area of $\Delta AFB$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the $\angle FAE$.</span></div></li></ol>

The diagram shows a prism whose cross-section area is a right-angled triangle.

$AB=24$ cm, $BC=8$ cm and $FC=6$ cm.

Basics of Trigonometric Ratios

Area of Triangle

Trigonometric Ratios in 3D: Determining the Inclination of Line $AF$

Perimeter and Area of Plane Figures

<p>The diagram above shows a triangular field $ABC$. $AB=45$ m, $BC=28$ m and angle $ABC$ is a right angle.<br>Calculate</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">angle $BAC$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">length $AC$.</span></div></li></ol>
<p>A pole $AD$ is planted perpendicular to the ground such that the angle of elevation of $D$ from $B$ is $40{}^\circ$.<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" start="3"><li><div class="list-item-paragraph">the height of the pole,</div></li><li><div class="list-item-paragraph">the angle of elevation of $D$ from $C$,</div></li><li><div class="list-item-paragraph">the area of triangle $BDC$.</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/1773462292483-lw4j1nnq2gh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzM0NjIyOTI0ODMtbHc0ajFubnEyZ2gucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNDc4MSwiZXhwIjoxNzkzNTA1MDgxfQ.fjpmfd2oM2K7u1DLGqKQjGcvQ7t1VngE05vAKkkr8Dk" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The diagram above shows a triangular field $ABC$. $AB=45$ m, $BC=28$ m and angle $ABC$ is a right angle.
Calculate

A pole $AD$ is planted perpendicular to the ground such that the angle of elevation of $D$ from $B$ is $40{}^\circ$.
Calculate

3D Trigonometry: Solving Angles of Elevation in a Non-Right Triangular Field

<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>The diagram shows a cuboid with a square base such that&nbsp;$AB=BC=5$ cm.<br>The height of the cuboid is $10$ cm.<br>Calculate</p><ol class="i-list"><li><div class="list-item-paragraph">$\angle EAB$,</div></li><li><div class="list-item-paragraph">$\angle DAC$.</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/1767441147837-a5k2kax1x2c.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0NDExNDc4MzctYTVrMmtheDF4MmMucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNDc4MSwiZXhwIjoxNzkzNTA1MDgxfQ.qB_apEgrlHe4YUnQtErDNOP6fCoo0VE-KpiexwcVPEw" style="max-width: min(170px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

3D Trigonometry: Geometric Analysis of a Square-Based Cuboid

<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>The diagram below shows a right square-base pyramid $PQRS$ with $PQ=13$ cm.<br>The midpoint of $RS$ is $M$.<br>The height $VO$ of the pyramid is $10$ cm.<br>Calculate</p><ol class="i-list"><li><div class="list-item-paragraph">the length of the diagonal $QS$,</div></li><li><div class="list-item-paragraph">the length $OM$,</div></li><li><div class="list-item-paragraph">the angle $VSQ$,</div></li><li><div class="list-item-paragraph">the volume of the pyramid.</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/1767440654797-2xe0n414n7j.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0NDA2NTQ3OTctMnhlMG40MTRuN2oucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNDc4MSwiZXhwIjoxNzkzNTA1MDgxfQ.NRFYRmHyEhn9spl35jsP-s9EVte_2dRhmTt0kD7M2VY" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Three-Dimensional Trigonometry: Analysis of a Right Square-Base Pyramid

<p>The diagram below shows a cuboid of dimensions $58$ cm by $42$ cm by $24$ 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">$BH$,</div></li><li><div class="list-item-paragraph">$\angle BHF$.</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/1767440140467-3slxzh9mt74.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0NDAxNDA0NjctM3NseHpoOW10NzQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNDc4MSwiZXhwIjoxNzkzNTA1MDgxfQ.UyokVR8I9-HgE9b3E7p3WTZxPUdQ0wwUSRX3sYPboQs" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The diagram below shows a cuboid of dimensions $58$ cm by $42$ cm by $24$ cm.

Trigonometric Applications in 3D Space: Solving for Cuboid Diagonals

<p>$A$, $B$, $C$ and $D$ are four points at sea level.<br>$A$ is due west of $B$, $AB=320$ m, $AD=132$ m, $BC=180$ m, $\angle ADC=48{}^\circ$.<br>The bearing of $B$ from $C$ is $160{}^\circ$.</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;"><ol class="abc-list"><li><div class="list-item-paragraph">Calculate</div><ol class="i-list"><li><div class="list-item-paragraph">the bearing of $C$ from $B$,</div></li><li><div class="list-item-paragraph">$\angle ABC$,</div></li><li><div class="list-item-paragraph">distance $CA$,</div></li><li><div class="list-item-paragraph">$\angle ACD$,</div></li><li><div class="list-item-paragraph">area of $\Delta ABC$.</div></li></ol></li><li><div class="list-item-paragraph">A boy stands on a vertical tower of height $35$ m at $C$ and looks at a boat travelling along $AB$. Find</div><ol class="i-list"><li><div class="list-item-paragraph">the shortest distance of $C$ to the boat.</div></li><li><div class="list-item-paragraph">the greatest angle of depression from $C$ to the boat.</div></li></ol></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/1767439445116-qbqce3n91s9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0Mzk0NDUxMTYtcWJxY2UzbjkxczkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNDc4MSwiZXhwIjoxNzkzNTA1MDgxfQ.Eth93adaMlOHfmXACI_Rsw__au07ixgBZZBhestLTcA" style="max-width: min(280px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

$A$, $B$, $C$ and $D$ are four points at sea level.
$A$ is due west of $B$, $AB=320$ m, $AD=132$ m, $BC=180$ m, $\angle ADC=48{}^\circ$.
The bearing of $B$ from $C$ is $160{}^\circ$.

Sine Rule

Cosine Rule

Bearings

3-Dimensional Problem

<p>The points $A$, $B$ and $C$ are on level ground and a flag pole is placed at point $A$ with the tip of the pole at $D$.<br>Given that the distance of $AB=80$ m, $AC=39$ m and $BC=74$ m.<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">the $\angle BAC$,</div></li><li><div class="list-item-paragraph">the area of $ABC$,</div></li><li><div class="list-item-paragraph">the height of the flag pole if the angle of elevation of the top of the flag pole when viewed from $B$ is $4{}^\circ$.</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/1767438594890-3hl1lqmcme.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0Mzg1OTQ4OTAtM2hsMWxxbWNtZS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTA0NzgxLCJleHAiOjE3OTM1MDUwODF9.HiKBjioCzuUrJLdtXNjal6e4gqzztgp0nMd1RLuscF4" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The points $A$, $B$ and $C$ are on level ground and a flag pole is placed at point $A$ with the tip of the pole at $D$.
Given that the distance of $AB=80$ m, $AC=39$ m and $BC=74$ m.
Calculate

<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 diagram shows a right-angled triangular prism.<br>$AB=24$ cm, $BC=10$ cm and $CE=7$ cm.<br>Find</p><ol class="i-list"><li><div class="list-item-paragraph">$AE$.</div></li><li><div class="list-item-paragraph">angle $DAF$.</div></li><li><div class="list-item-paragraph">angle $CAE$.</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/1767437806167-vzfi7u9gioe.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc0Mzc4MDYxNjctdnpmaTd1OWdpb2UucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MzUwNDc4MSwiZXhwIjoxNzkzNTA1MDgxfQ.gjNranfvSIhxUOZiWIO79rW9bY76I9dxUsZ4on016To" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

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