Question

Mia is standing 210 yd from a radio tower. The angle of elevation when she looks up to the top of the tower is 11°.

To the nearest tenth of a yard, how tall is the radio tower?

Answer 1

40.8 yd

Explanation:

From SOH CAH TOA, you know that the relationship between the adjacent side (distance to tower) and opposite side (height of tower) of the relevant triangle is given by ...

... tan(11°) = (height of tower)/(distance to tower)

Multiplying by the denominator, we have ...

... height of tower = (distance to tower) × tan(11°)

... = (210 yd) × 0.19438 ≈ 40.82 yd

Rounded to the nearest 0.1 yd, the height is 40.8 yd.