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Class 10 › Mathematics › Some Applications of Trigonometry
CBSE2026Class Class 10 · Mathematics5 Marks · Long✅ Verified
The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 60 m high, find the height of the building and distance between the building and the tower. (Use √3 = 1.73)
✅ Answer & Solution
Let height of building $=h$, distance between building and tower $=d$.
From foot of tower, elevation of building top is 30°: $\tan30°=\frac{h}{d} \Rightarrow h=\frac{d}{\sqrt3}$ ...(i)
From foot of building, elevation of tower top is 60°, tower height 60 m: $\tan60°=\frac{60}{d} \Rightarrow d=\frac{60}{\sqrt3}=20\sqrt3\ m$
From (i): $$h=\frac{20\sqrt3}{\sqrt3}=20\ m$$
Using $\sqrt3=1.73$: $d=20\times1.73=34.6\ m$. So height of building = 20 m and distance between building and tower = 34.6 m.
