Question

a ramp is being built next to a 4-inch high sidewalk. the ramps angle of inclination is 10 degrees. estimate the length of the ramp to the nearest tenth of an inch.
3.9 inches
0.7 inches
4.1 inches
22.7 inches

Explanation:

Step1: Identify trigonometric ratio

We use the sine function, since $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=10^\circ$, opposite side $=4$ inches, hypotenuse = ramp length $L$.
$\sin(10^\circ) = \frac{4}{L}$

Step2: Rearrange to solve for $L$

Isolate $L$ by cross-multiplying.
$L = \frac{4}{\sin(10^\circ)}$

Step3: Calculate the value

Use $\sin(10^\circ) \approx 0.1736$.
$L \approx \frac{4}{0.1736} \approx 22.7$

Answer:

22.7 inches