Question

A cat is watching a bird in a tree nearby. The tree is approximately 20 ft from the cat (ground distance). If the cat’s line of sight makes a 25° with the ground when he has his eye on the bird, how high up is the bird in the tree?
A. Draw a picture


B. Solve the problem, Solve to the nearest ft.

Answer 1

Answer:

9.3 feet

Step-by-step explanation:

See attachment for the picture.

Let f represent how high up the bird is in the tree.

This side length of the right triangle is opposite the given angle which is 25 degrees.

The side length adjacent to the given angle is 20 ft.

We use the tangent ratio to obtain:

$\tan 25\degree=\frac{opposite}{adjacent}$

We substitute the values to obtain:

$\tan 25\degree=\frac{f}{20}$

$f=20\tan 25\degree$

f=9.3 ft

Therefore the bird is 9.3 feet high up in the tree.