Question

question 5 (multiple choice worth 2 points) (triangle trigonometry mc) a wheelchair access ramp rises 2 feet over a distance of 27 feet. what is the angle of elevation for the ramp? 85.6° 26.5° 7.4° 4.2°

Explanation:

Step1: Recall tangent function in right - triangle

In a right - triangle formed by the ramp, the vertical rise is the opposite side ($y = 2$) and the horizontal distance is the adjacent side ($x = 27$) to the angle of elevation $\theta$. The tangent of an angle in a right - triangle is $\tan\theta=\frac{y}{x}$.
So, $\tan\theta=\frac{2}{27}$.

Step2: Find the angle

We need to find $\theta$. Using the inverse - tangent function, $\theta=\arctan(\frac{2}{27})$.
Calculating $\arctan(\frac{2}{27})\approx 4.2^{\circ}$ (using a calculator in degree mode).

Answer:

$4.2^{\circ}$