Question

1. calculate the angle of elevation and the slope of the hypotenuse.

a) 11 ft 25 ft
b) 29 cm 14 cm

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: Recall Pythagorean theorem for part 3a

For a right - triangle with legs \(a = 3\) and \(b = 7\), the length of the hypotenuse \(c\) (surface of the jump) is given by \(c=\sqrt{a^{2}+b^{2}}\).
\[c=\sqrt{3^{2}+7^{2}}=\sqrt{9 + 49}=\sqrt{58}\approx7.62\]

Step2: Recall tangent formula for part 3b

The tangent of the angle of elevation \(\theta\) in a right - triangle is \(\tan\theta=\frac{\text{rise}}{\text{run}}\). Here, \(\text{rise}=3\) and \(\text{run}=7\), 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 \(23.2^{\circ}\)