Question

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. 10° 18° 31° 80°

Explanation:

Step1: Recall sine - function in right - triangle

In a right - triangle, if the angle of elevation is $\theta$, the opposite side to the angle $\theta$ is $y = 80$ ft and the hypotenuse is $r=445$ ft. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{y}{r}$.

Step2: Calculate the sine of the angle

Substitute $y = 80$ and $r = 445$ into the sine formula: $\sin\theta=\frac{80}{445}\approx0.1798$.

Step3: Find the angle

To find the angle $\theta$, we use the inverse - sine function, $\theta=\sin^{- 1}(0.1798)$. Using a calculator, $\theta=\sin^{-1}(0.1798)\approx10^{\circ}$.

Answer:

$10^{\circ}$