Question

question
sydney wants to use a sheet of fiberboard 36 inches long to create a skateboard ramp with a 20°
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.
answer
inches
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Explanation:

Step1: Identify the trigonometric relationship

We know that in a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the hypotenuse \(c = 36\) inches and the angle \(\theta=20^{\circ}\), and we want to find the height \(y\) (opposite side to the angle \(\theta\)).

Step2: Apply the sine formula

Using the formula \(\sin\theta=\frac{y}{c}\), we can solve for \(y\). Substitute \(\theta = 20^{\circ}\) and \(c = 36\) into the formula: \(y=c\times\sin\theta\).
Since \(\sin(20^{\circ})\approx0.3420\), then \(y = 36\times0.3420\).

Step3: Calculate the value

\(y=36\times0.3420 = 12.312\)

Answer:

\(12.31\) inches