From a hot-air balloon, Justin measures a \( 34^{\circ} \) 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 Attempt 2 out of 2

We can model the situation with a right triangle where the horizontal distance (1424 feet) is the adjacent side and the vertical distance (the balloon's altitude) is the opposite side. The angle of depression from the balloon is 34°, which is congruent to the angle of elevation from the ground to the balloon. Using the tangent function for the angle:   tan(34°) = (vertical distance) / (horizontal distance) Solve for the vertical distance:   vertical distance = 1424 × tan(34°) Using a calculator:   tan(34°) ≈ 0.67451 Thus:   vertical distance ≈ 1424 × 0.67451 ≈ 960.50 feet So, the balloon's vertical distance above the ground is approximately 960.50 feet.