Question

shellyara is hiking a straight line up a mountain trail. she hikes a total of 9 miles to gain 3 miles of elevation. what is the angle of elevation of the mountain trail? 71.6° 70.53° 19.47° 18.43°

Explanation:

Step1: Identify the trigonometric ratio

We know that the sine of an angle in a right - triangle is given by \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the opposite side (elevation) \(y = 3\) miles and the hypotenuse (distance hiked) \(h=9\) miles. So, \(\sin\theta=\frac{3}{9}=\frac{1}{3}\).

Step2: Find the angle

To find \(\theta\), we use the inverse sine function \(\theta=\sin^{- 1}(\frac{1}{3})\). Using a calculator, \(\theta=\sin^{-1}(\frac{1}{3})\approx19.47^{\circ}\)

Answer:

19.47°