If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a foot?

distance of his partner from the base of the tower ≈ 53.6 ft

Step-by-step explanation:

The forest ranger is on top of a fire tower and he sees his partner on the ground at the angle of depression of 40°. The tower is 45 ft tall.  

The illustration forms a right angle triangle.

The adjacent side of the triangle is the distance from the partner to the base of the tower.

Using tangential ratio

tan 40° = opposite/adjacent

tan 40° = 45/adjacent

cross multiply

adjacent tan 40° = 45

divide both sides by tan 40°

adjacent =45/tan 40°

adjacent = 45/0.83909963117

adjacent = 53.6289116667

(3x-8) or (3x+8)

step-by-step explanation: