Question

adriel wants to use a sheet of fiberboard 25 inches long to create a skateboard ramp with a 16° 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: Identify trigonometric ratio

The ramp forms a right triangle where the hypotenuse is 25 inches, the angle of elevation is 16°, and the height \(x\) is the opposite side to the angle. Use sine: \(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Substitute values

\(\sin(16^\circ) = \frac{x}{25}\)

Step3: Solve for x

\(x = 25 \times \sin(16^\circ)\)

Step4: Calculate the value

Using a calculator, \(\sin(16^\circ) \approx 0.2756\), so \(x \approx 25 \times 0.2756 = 6.89\)? Wait, correction: precise calculation gives \(\sin(16^\circ) \approx 0.2756373558\), \(25×0.2756373558≈6.8909≈6.89\)? Wait no, wait another check: 16 degrees sine is approximately 0.2756, 250.2756=6.89. Yes, correct. (Note: some calculators may have slight variations but rounded to nearest hundredth is 6.89 or 6.90? Wait let's compute exactly: 16 degrees in radians is about 0.2793 radians, sine(0.2793)≈0.2756, so 250.2756=6.89. So final answer is 6.89 inches.)

Wait correction: Let me confirm again. Using calculator input: sin(16) = sin(16°) ≈ 0.27563735581699916. Multiply by 25: 25 * 0.27563735581699916 = 6.890933895424979. Rounded to nearest hundredth is 6.89 inches. So the answer is 6.89 inches.

Step1: Choose sine ratio

\(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\)

Step2: Substitute values

\(\sin(16^\circ)=\frac{x}{25}\)

Step3: Solve for x

\(x=25\times\sin(16^\circ)\)

Step4: Compute result

\(x≈25×0.2756≈6.89\)

Answer:

6.97 inches