Question

determining an angle of elevation
a car is traveling up a steep ramp to a parking garage. the ramp is 445 feet long and rises a vertical distance of 80 feet. what is the angle of elevation from the car to the end of the ramp? round to the nearest degree.
445 ft
80 ft

Explanation:

Step1: Identify the trig - function

We have a right - triangle where the hypotenuse is the length of the ramp ($c = 445$ ft) and the opposite side to the angle of elevation $\theta$ is the vertical rise ($a = 80$ ft). We use the sine function $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine value

$\sin\theta=\frac{80}{445}\approx0.1798$.

Step3: Find the angle

$\theta=\sin^{- 1}(0.1798)$. Using a calculator, $\theta\approx10^{\circ}$.

Answer:

$10^{\circ}$