Question

question faith wants to use a sheet of fiberboard 24 inches long to create a skateboard ramp with a 26° angle of elevation from will the ramp rise from the ground at its highest end? round your answer to the nearest tenth of an inch if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use sine, since $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=26^\circ$, hypotenuse $=24$, opposite side $=x$.
$\sin(26^\circ)=\frac{x}{24}$

Step2: Solve for $x$

Rearrange to isolate $x$: multiply both sides by 24.
$x=24\times\sin(26^\circ)$

Step3: Calculate the value

Compute $\sin(26^\circ)\approx0.4384$, then multiply by 24.
$x\approx24\times0.4384=10.5216$

Step4: Round to nearest tenth

Round 10.5216 to one decimal place.
$x\approx10.5$

Answer:

10.5 inches