Question

From a hot-air balloon, Justin measures a 34 ∘ angle of depression to a landmark that’s 1424 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.

Answer 1

923.93 feet

Explanation:

To find the vertical distance above the ground, we can use the tangent function, which relates the angle of depression to the ratio of the vertical distance to the horizontal distance.

Given:

Angle of depression = 34 degrees

Horizontal distance = 1424 feet

Let's denote the vertical distance as "d" (in feet).

Using the tangent function:

tan(angle) = vertical distance / horizontal distance

tan(34°) = d / 1424

To find "d," we can rearrange the equation:

d = tan(34°) * 1424

Calculating the value:

d ≈ 0.6494 * 1424

d ≈ 923.93

Therefore, the balloon's vertical distance above the ground is approximately 923.93 feet.