Question

Two birds sit at the top of two different trees 57.4 feet away from one another. the distance between the second bird and a birdwatcher on the ground is 49.6 feet. what is the angle measure, or angle of depression, between the first bird and the birdwatcher? two trees that are 49 point 6 feet tall with a bird on top of each. distance between the birds is 57 point 4 feet. angle of depression between birdwatcher and first bird is unknown. © 2011 jupiter images corporation 30.2° 59.8° 40.8° 49.2°

Answer 1

The angle measure, or angle of depression, between the first bird and the birdwatcher, is (C) 40.8°.

What is the angle of depression?

• The angle of depression is the angle formed by the horizontal line and the item as seen from the horizontal line.
• It is mostly used to calculate the distance between two objects where the angles and distance from the ground are known.
• For example, if you're standing on the ground and looking up at the peak of a mountain, you may calculate the angle of elevation.
• The angle of depression is defined as the angle formed by the horizontal line of sight and the downward line of sight to an object.

To find the angle of depression in the given situation:

• First, we must sketch the problem. The graphic linked depicts the right triangle generated by these three birds using each supplied value.
• It is critical to understand that the angle of depression is the angle formed by the horizontal and diagonal at the top, as shown in the image.

We now employ trigonometric reasoning, notably the tangent function, which connects both legs.

• $tan(x)=\frac{49.6}{57.4}$ ≈ $0.86$
• $x$ ≈ $tan^{-1} (0.86)$
• $x$ ≈ $40.8^{o}$

Therefore, the angle measure, or angle of depression, between the first bird and the birdwatcher, is (C) 40.8°.

Know more about the angle of depression here:

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The correct question is given below:

Two birds sit at the top of two different trees 57.4 feet away from one another. the distance between the second bird and a birdwatcher on the ground is 49.6 feet. what is the angle measure, or angle of depression, between the first bird and the birdwatcher? two trees that are 49 points 6 feet tall with a bird on top of each. The distance between the birds is 57 point 4 feet. the angle of depression between a birdwatcher and the first bird is unknown. © 2011 Jupiter images corporation

(A) 30.2°

(B) 59.8°

(C) 40.8°

(D) 49.2°