Question

27. If the distance of a point from the base of a building is 15 m and angle of elevation to its top from that point is 60°. Then, what is the height of the building? (a) 25 m (b) 26 m (c) 31 m (d) 18 m​

Answer 1

Given: Distance of a point from base of a building is 15m and angle of elevation to its top from that point is 60°.

To find: Height of the building

Explanation: Let ABC be a triangle with A as the top point of building, B be the point from where building is seen and C be the base of the building.

Now, distance of point from base= 15 m

=> BC= 15 m

Angle ABC= 60°

Now, in triangle ABC:

tan 60° = Height of building/ distance between point and base

=> $\sqrt{3} = \frac{height}{15}$

=>$height = 15 \sqrt{3}$

=> height = 15 * 1.73

=> height= 25.95 m which can be rounded to 26 m.

Therefore, the height of the building is 26 m.