Question

a skateboarding ramp is 11 in. high and rises at an angle of 15°. how long is the base of the ramp? round to the nearest inch.

the base of the ramp is \\(\square\\) inches.
(round to the nearest integer as needed.)

Explanation:

Step1: Define trigonometric relation

We use the tangent function: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, where $\theta=15^\circ$, opposite side = 11 in, adjacent side = base length $b$.

Step2: Rearrange to solve for base

Rearrange the formula to isolate $b$: $b = \frac{11}{\tan(15^\circ)}$

Step3: Calculate the value

First, $\tan(15^\circ) \approx 0.2679$. Substitute: $b \approx \frac{11}{0.2679} \approx 41.06$

Step4: Round to nearest inch

Round 41.06 to the nearest whole number.

Answer:

41