In this task, you’ll apply what you’ve learned to answer questions about a skateboard ramp that you and your friends are building for your community skate park. The ramp will lead up to a platform. You’ll be using a piece of wood that’s 3.5 meters long for the ramp, and the ramp’s angle of elevation will be 28°. Use this figure as a model to answer the questions that follow. -One friend claims that to find the height of the platform, you need to use the tangent ratio. Explain why her approach is or is not a reasonable approach to finding the height of the platform.
-Find the height of the platform. Explain the trigonometric ratio that you chose to use and why you chose it. Show your work, rounding to the nearest hundredth, if necessary.
-Find the horizontal distance from the bottom of the ramp to the bottom of the platform. Show your work, rounding to the nearest hundredth, if necessary.
-Another friend claims that you can use the cosine ratio to find the height of the platform. Explain why his approach is or isn’t a reasonable approach to finding the height of the platform.
-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 . 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