Trigonometry

Question

Josh found two trees directly across from each other in a canyon. When he moved 100 feet from the tree on his side (parallel to the edge of the canyon), the angle formed by the tree on his side and the tree on the other side was 70 degrees. Find the distance across the canyon

Answer 1

Draw and label a diagram.

 

A right triangle is formed.

d represents the distance between the two trees, one of the legs

100 is the length of the other leg.

70° is the angle between the other leg and the hypotenuse

 

tan 70° = d/100

2.7474 ≈ d/100

274.74 ≈ d

 

The distance between the two trees is approximately two hundred seventy-four and seventy-four hundredths feet.