Two horses are observed by a hang glider 80 meters above a meadow. The angles of depression to the horses are 10.4 degrees and 8 degrees. How far apart are the horses?

Question

Round answer to the nearest tenth

Answer 1

Draw and label a diagram! That includes all angles

A is the location of the closer horse

B is the location of the farther horse

x is the distance between A the the point under glider.

tan 10.4° = 80 / x

x tan 10.4° = 80

x = 80 / tan 10.4°

tan 8° = 80 / (x + AB)

(x + AB) tan 8° = 80

x tan 8° + AB tan 8° = 80

x tan 8° = 80 - AB tan 8°

x = (80 - AB tan 8°) / tan 8°

Set the two expressions equal to x equal to each other and solve for AB