Question

David is building a bike ramp. He wants the angle that the ramp makes with the ground to be 20. If the board he wants to use for his ramp is 3 1/2 feet long, about how tall will the ramp need to be at the highest point?

Answer 1

To find the height at the highest point of the bike ramp, use the sine function with the ramp length and the angle. The calculation reveals that the height is approximately 1.19 feet.

Step-by-step explanation:

The student's question requires a calculation based on trigonometric functions to find the height of a bike ramp. Given that the ramp makes a 20-degree angle with the ground and has a length of 3.5 feet, we can use the sine function to find the height at the highest point.

Step-by-Step Calculation

1. Identify the angle given: 20 degrees.
2. Identify the length of the ramp, which is the hypotenuse in this right-angle triangle scenario: 3.5 feet.
3. Use the sine function to calculate the height (opposite side in the triangle), which is:
   height = ramp length (hypotenuse) × sin(angle).
4. Perform the calculation with the provided values: height = 3.5 feet × sin(20 degrees).
5. Use a calculator to find the sine of 20 degrees and multiply by 3.5 to find the height.

The calculation yields approximately 1.19 feet for the height at the highest point of the ramp. Thus, David will need to make sure that the highest point of his ramp is about 1.19 feet off the ground to achieve the desired 20-degree angle with the ground.