Question

Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 30 feet. The distance between the birdwatcher and the second bird is 43 feet. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth.

34.9°
44.2°
45.8°
55.1°

Answer 1

44.2°

Explanation:

Givens

• The distance between the first bird and a birdwatcher is 30 feet.
• The distance between the birdwatcher and the second bird is 43 feet.

Notice that the hypothenuse is 43 feet long and the opposite leg to angle
`x` is 30 feet.

So, we can find the angle using the sine function,

`sin(x\°)=(30ft)/(43ft) \approx 0.7\\ x\° \approx sin^(-1)(0.7) \\x\° \approx 44.2\°`

Therefore, the right answer is the second choice.

Answer 2

44.2°

Explanation:

We want to find the angle x. We know the side opposite of the angle (30 feet) and the hypotenuse (43 feet). So we should use sine.

sine = opposite / hypotenuse

sin x = 30 / 43

x = 44.2°