Question

From a window, 29.6 m above the ground, the angle of elevation of the top of a building is 42˚, while the angle of depression to the foot of the building is 32˚. Find the height of the building.

Answer 1

Now, first of all, we will calculate the distance between A and B.

For that, we have:

tanØ = perpendicular / base

tan32° = 29.6m / b

b tan32° = 29.6m

b = tan^-1 (32°) × 29.6m

b = 45.57m

Now, we will calculate the distance between B and C.

For that, we have:

tanØ = perpendicular / base

tan42° = x / 45.57m

x = tan42° × 45.57m

x = 104.41855m

Now, the height of the building is:

h = x + 29.6m

h = 104.41855m + 29.6m

h = 134.08155m