Question

question
elizabeth wants to use a sheet of fiberboard 27 inches long to create a skateboard ramp
with a 17° 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 tenth of an inch if
necessary.
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Explanation:

Step1: Identify the trigonometric relationship

We can use the sine function. The formula for sine in a right - triangle is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the hypotenuse is the length of the ramp (\(c = 27\) inches) and the angle of elevation \(\theta=17^{\circ}\), and the height \(h\) (opposite side) is what we want to find.

Step2: Substitute values into the sine formula

We know that \(\sin\theta=\frac{h}{c}\). Substituting \(\theta = 17^{\circ}\) and \(c = 27\) inches, we get \(h=c\times\sin\theta\). Since \(\sin(17^{\circ})\approx0.292\) (using a calculator), then \(h = 27\times\sin(17^{\circ})\).

Step3: Calculate the value of \(h\)

\(h=27\times0.292 = 7.884\) inches. Rounding to the nearest tenth of an inch, we look at the second decimal digit. Since \(8\gt5\), we round up.

Answer:

\(7.9\) inches