Question

From a point 80m from the base of a tower, the angle of elevation to the top of the tower is 28 degrees how tall is the tower

Answer 1

The height of the tower is 42.54 m.

Solution:

The reference image of the answer is attached below.

Given data:

BC = 80 m, ∠C = 28°

$\tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}$

$\tan28^\circ = \frac{AB}{BC}$

$\tan28^\circ = \frac{h}{80}$

$0.5317 = \frac{h}{80}$

Multiply by 80 on both sides, we get

42.536 = h

Switch the sides.

h = 42.536

h = 42.54 m

The height of the tower is 42.54 m.