Question

A bird at the top of a tree looks down at a field mouse with an angle of depression of 65Á. If the field mouse is 30 meters from the base of the tree, find the distance from the field mouse to the birdÍs eyes. Round the answer to the nearest tenth.

a.
29.6 m
b.
50.0 m
c.
64.3 m
d.
71.0 m

Answer 1

The distance from the field mouse to the bird's eyes is approximately 64.3 meters.

Step-by-step explanation:

To find the distance from the field mouse to the bird's eyes, we can use trigonometry. Given that the angle of depression is 65 degrees and the mouse is 30 meters from the base of the tree, we can use the tangent function to calculate the distance. The tangent of the angle of depression is equal to the opposite side (the height of the tree) divided by the adjacent side (the distance from the tree to the mouse). So, tan(65) = opposite/30. Solving for the opposite side gives us: opposite = 30 * tan(65). Using a calculator, we find that the distance from the field mouse to the bird's eyes is approximately 64.3 meters.

Answer 2

Correct answer is 33.1 m.

Use The definition of trigonometric functions. The sine of an angle is the quotient of the opposite side and hypotenuse.


`sin{65^o}= (30)/(x) \\x= \frac{30}{sin{65^o}} \\x=33.1`