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<p>A farmer owns two triangular plots of land \(ABC\) and \(ADC\) as shown in the diagram above. It is given that&nbsp;\(AB=7\) m, \(AC=8\) m and \(AD=6\) m, \(\angle BAD\) is a right angle and \(\angle BAC=\theta\) radians.</p>
<ol class="abc-list"><li><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show the total area of the two plots of land, \(A\) m\({}^2\), can be expressed in the form \(a\sin\theta + b\cos\theta\), where&nbsp;\(a\) and \(b\) are integers.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Express A in the form of \(R\sin(\theta +\alpha)\) where&nbsp;\(R &gt; 0\) and \(0 &lt; \alpha  &lt;\frac{\pi}{2}\)<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the greatest possible value of <strong>A</strong> and the value of \(\theta\) at whcih this occurs.<span class="inline-marks">[3]</span></div></li></ol></li><li><div class="list-item-paragraph">The farmer would like to grow ross on plot <strong>ABC</strong> and hibiscus on plot <strong>ADC</strong>. Given that he wants the area of plot <strong>ABC</strong> to be twice the area of plot <strong>ADC</strong>, find the value of \(\theta\).<span class="inline-marks">[3]</span></div></li></ol>

A farmer owns two triangular plots of land \(ABC\) and \(ADC\) as shown in the diagram above. It is given that \(AB=7\) m, \(AC=8\) m and \(AD=6\) m, \(\angle BAD\) is a right angle and \(\angle BAC=\theta\) radians.

Show the total area of the two plots of land, \(A\) m\({}^2\), can be expressed in the form \(a\sin\theta + b\cos\theta\), where \(a\) and \(b\) are integers.

The farmer would like to grow ross on plot **ABC** and hibiscus on plot **ADC**. Given that he wants the area of plot **ABC** to be twice the area of plot **ADC**, find the value of \(\theta\).

2025 CGSS PRELIMS P2 Q9

2025 CGSS PRELIMS P2 Q9