Trigonometry & Inverse Trigonometry
Double Angle of Depression — Area of Quadrilateral
nta_pyq_2023_apr
Grade 11
Question:
From the top $A$ of a vertical wall $AB$ of height 30 m, the angles of depression of the top $P$ and bottom $Q$ of a vertical tower $PQ$ are $15°$ and $60°$ respectively, $B$ and $Q$ are on the same horizontal level. If $C$ is a point on $AB$ such that $CB=PQ$, then the area (in m²) of the quadrilateral $BCPQ$ is equal to
300(\sqrt{3}-1)
300(\sqrt{3}+1)
600(\sqrt{3}-1)
200(\sqrt{3}-1)
Step-by-Step Solution
Key Concept: $\tan60°=\frac{AB}{BQ}\Rightarrow BQ=10\sqrt{3}$. $\tan15°=\frac{AC}{BQ}\Rightarrow h=AC=AB-BC=60-20\sqrt{3}$.
$h=60-20\sqrt{3}$, $BQ=10\sqrt{3}$. Area $=600(\sqrt{3}-1)$ m².
Correct Answer: 3