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

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.

$sin{65^o}= \frac{30}{x} \\x= \frac{30}{sin{65^o}} \\x=33.1$