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.

Question

1 month ago

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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. A triangle is created from point Bird Watcher, point First Bird, and point Second Bird. Angle First Bird is a right angle, and angle Second Bird measures x degrees. 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°

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-04-11T19:24:34+03:00

Response:

Step-by-step breakdown:

When you sketch that diagram (great description, by the way!), what you essentially have is a right triangle with a base of 32 and a hypotenuse of 45. The right angle resides at one of the base's ends, and x represents the vertex angle. We must find this vertex angle first to determine the angle of depression from the second bird to the watcher. The side measuring 32 is opposite to angle x, with 45 being the hypotenuse; hence, the trigonometric relation we need is sine:

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

sin(x) =.711111111

Go to your calculator, press the 2nd key followed by the sin key, and your display will show:

$sin^{-1}($

then, enter in your decimal.711111111 and hit equals. You should arrive at an angle of 45.325. That angle is x. However, that's not the angle of depression. The angle of depression is the complementary angle to x.

Angle of depression = 90 - angle x and

Angle of depression = 90 - 45.325, resulting in

Angle of depression = 44.67 or 44.7 degrees.