After testing out your skateboard ramp, you and your friends decide that it’s too steep. You decide to redesign the ramp so that the angle of elevation is only 20 degrees. However, you want the length of the ramp to stay the same. In the new design, about how much farther will the ramp extend horizontally from the platform than in the original design? Show the steps that justify how you arrived at your answer.

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AvarieG131286 AvarieG131286 · Answer 1 · 2022-10-30T10:54:58+01:00

Explanation,

To solve the question, we will have the sketch

Since the ramp is 3.5m in length

Then

AB = FB = 3.5m

Our task will be to get FA

To do so, we will have to get AC and FC

so that

FA = FC - AC

Thus, we will have to get AC first

[tex]\begin{gathered} cos28=\frac{AC}{ramp}=\frac{AC}{3.5} \\ \\ AC=3.5\times cos28 \\ \\ AC=3.090m \end{gathered}[/tex]

Next, we will get FC

[tex]\begin{gathered} cos20=\frac{FC}{ramp}=\frac{FC}{3.5} \\ \\ FC=3.5\times cos20 \\ \\ FC=3.289m \end{gathered}[/tex]

Therefore

[tex]FA=3.289m-3.090m\text{ =0.199 m}[/tex]

Therefore, the ramp will need to extend 0.199m further