Question

1. a ski jump rises 3 feet over a run of 7 feet.

a) what is the length of the surface of the jump?
b) what is the angle of elevation of the jump?

Explanation:

Step1: Use Pythagorean theorem for part a

The ski - jump forms a right - triangle, where the rise (\(a = 3\) feet) and run (\(b=7\) feet) are the legs, and the surface of the jump (\(c\)) is the hypotenuse.
By the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\).
Substitute \(a = 3\) and \(b = 7\): \(c^{2}=3^{2}+7^{2}=9 + 49=58\).
Then \(c=\sqrt{58}\approx7.62\) feet.

Step2: Use trigonometric ratio for part b

Let \(\theta\) be the angle of elevation.
We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\), where the opposite side is the rise (\(a = 3\)) and the adjacent side is the run (\(b = 7\)).
So \(\tan\theta=\frac{3}{7}\).
Then \(\theta=\arctan(\frac{3}{7})\approx23.2^{\circ}\)

Answer:

a) The length of the surface of the jump is approximately 7.62 feet.
b) The angle of elevation of the jump is approximately \(23.2^{\circ}\).