Question

A bird is flying at an altitude of 400 feet and descending to its nest located in a tree 20 feet above the ground. The angle from the nest to the bird is 24 degrees. Approximately how far is the bird from the nest.

Answer 1

936m

Explanation:

What we have here is a rght triangle, where one leg is the hight between the nest and the bird (400 - 20 =380) and the other is the distance between the bird and the nest linearly from the ground (name it X). The hypotenuse is the distance the bird will fly ( name it H).

Is not clear if we need to find X or H so we will find both.

First, to find H we use the trigonometric formula:

Sin(24) = leg opposed / hypotenuse

Sin(24) is 0.406 aprox

So,

0.406 = 380/h -> h = 380/0.406 = 936 (aprox)

Then we find X, the adjacent leg to 24° using the formula:

Cos(24) = X / hypotenuse

Cos(24) is approximately 0.91

So:

0.91 = X / 936 -> X=0.91*936= 852 (aprox)

So, the distance ir 936 ir 852, depending on what you need. The statement is not very clear (however I guess it is 936 as is the distance the bird Weill fly)