From a hot-air balloon, Nayeli measures a 35degrees∘ angle of depression to a landmark that’s 905 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.
We can use trigonometric functions to solve this problem. The angle of depression is the angle from the horizontal to a line of sight from an observer to a point below the observer. In this case, Nayeli is in the hot-air balloon and the landmark is below her.
Let's represent the vertical distance of the balloon above the ground as "x" feet. Then, we can set up a right triangle where the hypotenuse is the horizontal distance to the landmark (905 feet) and the vertical side is x feet.
Using the definition of tangent, we can write:
tan(35°) = x / 905
To find x, we can multiply both sides of the equation by 905 and then take the tangent of 35°:
x = 905 * tan(35°)
Using a calculator, we find:
x ≈ 905 * 0.700207538
x ≈ 633.12
Therefore, the balloon's vertical distance above the ground is approximately 633.12 feet.