Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 136.6 m
The angle of elevation of the top of a tower seen from a point on the ground satisfies \(\tan\theta=\frac{\text{height}}{\text{distance from the foot}}\). The men stand on opposite sides of the tower, so their two distances from the foot are added.
From C (\(\tan45^\circ=1\)):
\(\tan45^\circ=\frac{50}{CB}\)
\(CB=50\,\mathrm{m}\)
From D (\(\tan30^\circ=\frac{1}{\sqrt{3}}\)):
\(\tan30^\circ=\frac{50}{BD}\)
\(BD=50\sqrt{3}\approx50\times1.732=86.6\,\mathrm{m}\)
Distance between the men (on opposite sides, so the two distances are added):
\(CB+BD=50+86.6=136.6\,\mathrm{m}\)