Question

A climber is ascending the face of a 500-foot high vertical cliff at 5 feet per minute. Her climbing partner is observing from 150 feet away. Find the function that describes the amount of time climbing as a function of the angle of elevation of the observer’s line-of-sight to the climber. Does the viewing angle ever reach 75 degrees?

Answer 1

a) t (α) = 30 * tan α

b) α = 75 ° is not possible because

Explanation:

The vertical cliff (y), the observing partner ( 150 ft ) from the point o ( the common point for the cliff and the ground ) between the cliff, and the line of sight from the observer and the climber, shape a right triangle. Hypothenuse is the distance between the partners, the cliff, and distance of the observer to the cliff are the legs.

Then

α is the elevation angle

tan α = y / 150 (1)

y(t) = elevation of the climber

y(t) = speed * time

y(t) = 5 * t

tan α = 5 *t / 150

tan α = t / 30

t (α) = 30 * tan α

b) α = 75 ° is not possible because:

tan α = y / 150 tan 75° = 3.73

Then y = 3.73 * 150 = 559 ft and the cliff is only 500 ft