Answer:
distance of his partner from the base of the tower ≈ 53.6 ft(nearest tenth)
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
distance of his partner from the base of the tower ≈ 53.6 ft