Question

Rhian is 9.2 meters up, and the angle of depression from Rhian to Mary is 79. Find the distance from Mary to the base of the building to the nearest tenth of a meter.

Options:
a. 24.5 meters,
b. 28.7 meters,
c. 32.1 meters,
d. 35.6 meters

Answer 1

The distance from Mary to the base of the building, using the angle of depression of 79 degrees and Rhian’s height of 9.2 meters, is approximately 24.5 meters, which is option (a).

Step-by-step explanation:

The student needs to find the distance from Mary to the base of the building, given Rhian's height above the ground and the angle of depression. Using trigonometry, we can solve this problem with the tangent function, since the angle of depression is the same as the angle of elevation from Mary to Rhian:

Tan(angle) = Opposite/Adjacent, which rearranges to Adjacent = Opposite/Tan(angle).

Here, Opposite is Rhian's height (9.2 meters), and the angle is 79 degrees. Plugging these values into the equation:

Adjacent = 9.2 / Tan(79 degrees)

The calculated distance (Adjacent) will be the distance from Mary to the base of the building. Using a calculator, we find that the distance is approximately 24.5 meters, which corresponds to option (a).