Question

question
suav wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp with a 19° angle of elevation from the ground. how high will the ramp rise from the ground at its highest end? round your answer to the nearest hundredth of an inch if necessary.

Explanation:

Step1: Define trigonometric relationship

The ramp forms a right triangle where the fiberboard length is the hypotenuse ($c=27$ inches), the height $h$ is the opposite side to the $19^\circ$ angle. Use $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(19^\circ) = \frac{h}{27}$

Step2: Solve for height $h$

Rearrange the formula to isolate $h$.
$h = 27 \times \sin(19^\circ)$

Step3: Calculate numerical value

Use a calculator to find $\sin(19^\circ) \approx 0.3256$, then compute $h$.
$h \approx 27 \times 0.3256 = 8.7912$

Step4: Round to nearest hundredth

Round the result to two decimal places.
$h \approx 8.79$

Answer:

8.79 inches