Question

Mia is standing 210 yd from a radio tower.

The angle of elevation from where she is standing on the ground to the top of the tower is 11°.
How tall is the radio tower?
Round the final answer to the nearest tenth. Enter in blank space.

____ yd?

Answer 1

The height of the radio tower is 40.8 yd.

Step-by-step explanation:

Let us draw a diagram for the given situation. In the attached diagram AB is the radio tower and Mia is standing at point C.

The angle of elevation is 11°. Hence, angle C is 11°.

Let the height of the tower is h.

In triangle ABC, we have

`\tan \theta = (AB)/(BC) \\\\\tan 11^(\circ)=(h)/(210) \\\\h=210\tan 11^(\circ)\\\\h=40.8`

Therefore, the height of the radio tower is 40.8 yd.

Answer 2

height = tan(11) x 210

height = 40.81 yards

rounded to nearest tenth = 40.8 yards