From a point P on the ground, the angle of elevation of the top of a 10 m high building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from the point P is 45°. The length of the flagstaff is:
(Take \(\sqrt{3}=1.732\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7.32 m
The building, the flagstaff on it and the ground form two right triangles with the same base PC. The 30° angle and the 10 m building give PC; the 45° angle then gives the full height AC, and the flagstaff is AC minus the building.
Distance PC (triangle PCB, angle 30°):
\(\displaystyle\tan30^\circ=\frac{BC}{PC}=\frac{10}{PC}\), and \(\tan30^\circ=\frac{1}{\sqrt3}\)
\(PC=10\sqrt3\) m
Height AC (triangle PCA, angle 45°):
\(\tan45^\circ=1\), so \(AC=PC=10\sqrt3=10\times1.732=17.32\) m
Flagstaff \(h=AC-BC=17.32-10=7.32\) m