Question

Jill is standing at the base of her apartment building. She measures the angle of elevation to the top of a nearby tower to be 40º. Then Jill goes to the roof of her apartment building, directly above her previous position, and measures the angle of elevation to the top of the same tower to be 30°. If the height of the tower is 100 meters, the height of Jill's apartment building is:

A) 57.7 meters
B) 70.7 meters
C) 86.6 meters
D) 50.0 meters

Answer 1

The height of Jill's apartment building is approximately 57.7 meters.

Step-by-step explanation:

The height of Jill's apartment building can be determined using trigonometry. Let's denote the height of Jill's apartment building as h. Since Jill is directly above her previous position on the roof, the distance between her position and the tower remains the same. Let's denote this distance as d. Using trigonometric relationships, we can set up the following equation:

Tan(30°) = (h + 100) / d

Tan(40°) = h / d

By substituting the given values, we get:

Tan(30°) = (h + 100) / d

Tan(40°) = h / d

Solving these equations simultaneously, we find that h is approximately 57.7 meters.