Question

The angle of depression from a hot air balloon to its landing spot is 12 degrees. If the balloon is 175 ft high, find its horizontal distance (measured along the ground) to the landing spot.

a) 486 ft
b) 308 ft
c) 165 ft
d) 402 ft

Answer 1

To find the horizontal distance from the hot air balloon to the landing spot, use the tangent function to solve for the adjacent side.

Step-by-step explanation:

To find the horizontal distance from the hot air balloon to the landing spot, we can use the tangent function. The angle of depression is the angle between the horizontal ground and the line of sight from the balloon to the landing spot. Since we know the angle of depression is 12 degrees and the height of the balloon is 175 ft, we can use the equation: tan(angle) = opposite/adjacent. In this case, the opposite side is the height of the balloon and the adjacent side is the horizontal distance we want to find.

tan(12) = 175/adjacent

Solving for the adjacent side, we get: adjacent = 175/tan(12)

we find that the horizontal distance is approximately 486 ft. Therefore, the correct answer is option a) 486 ft.