Question

A truck parked on the street is 56 m from the base of the apartment building on the right. The angle of elevation from the truck to the top of the building is 40°. The parked truck is 49 m from the base of the apartment building on the left. The angle of elevation from the truck to the top of that building is 50°. Which building is taller?

Answer 1

Building to the left is taller.

Explanation:

Kindly refer to the attached diagram for the given dimensions.

`\triangle ABR, \triangle PQR`

AB and PQ be the two buildings.

The car be parked at point R.

`\angle ARB = 50^\circ\ and \\\angle PRQ = 40^\circ`

Distance of R from building bases:

BR = 49 m

QR = 56 m

Let us use tangent in
`\triangle PQR:`

`tan\theta = (Perpendicular)/(Base)`

`tan40 = (h_1)/(56)\\\Rightarrow h_1 = 56 * 0.839 \\\Rightarrow h_1 \approx 47\ m`

Let us use tangent in
`\triangle PQR:`

`tan\theta = (Perpendicular)/(Base)`

`tan50 = (h_2)/(49)\\\Rightarrow h_2 = 49 * 1.19 \\\Rightarrow h_2 \approx 58.4\ m`

So, building to the left is taller.