Question

Please help!! Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth. 35.4° 44.7° 45.3° 54.6°

Answer 1

Answer:

45.3°

Step-by-step explanation:

A right triangle is formed given the information above.

Angle of depression = x°

Distance between first bird and birdwatcher = opposite to angle x° = 32 ft

Distance between second bird and birdwatcher = hypotenuse of the right triangle formed = 45 ft

The trigonometric ratio formula to use is:

$sin(x) = \frac{opp}{hypo}$

$sin(x) = \frac{32}{45}$

$sin(x) = 0.7111$

$x = sin^{-1}(0.7111)$

$x = 45.3$ (nearest tenth)

Angle of depression = 45.3°