Question

What is the correct equation to find the distance, dd, in feet, from the basket of the hot air balloon to the base of the monument given that the hot air balloon is 1200 feet above the ground and the angle of depression from the basket to the base of the monument is 54°?

A. sin⁡54∘=d/ 1200
B. sin⁡54∘=1200/d
C. cos⁡54∘=d/1200
D. cos⁡54∘=1200/d

Answer 1

The correct equation to find the distance from the basket of the hot air balloon to the base of the monument when given the angle of depression and the altitude is C. cos​54° = d/1200, which can be rearranged to find d as d = 1200 ⋅ cos​54°.

Step-by-step explanation:

To find the distance from the basket of the hot air balloon to the base of the monument, we need to understand the relationship between the angle of depression, the altitude of the balloon, and the distance to the monument. Since the angle of depression is equal to the angle of elevation when measured from the ground, we can use trigonometric functions to determine the correct relationship.

Here, we know that the balloon is 1200 feet above the ground, and the angle of depression from the basket to the base of the monument is 54 degrees. This scenario creates a right triangle with the distance d as the adjacent side to the angle, the height of the balloon as the opposite side, and the angle as the angle formed between the horizontal and the line of sight from the balloon to the monument.

The cosine function relates the adjacent side to the hypotenuse in a right-angled triangle. Thus, the correct equation to find the distance d would be:

C. cos​54° = d/1200

This can be rearranged to find d:

d = 1200 ⋅ cos​54°