1. A skateboard ramp of 45° must be 4 ft. wide. The max height is 7 ft. How high should I build the ramp so that I can avoid fractions ?
the height will be equal to the width
thank you oobleck ! i appreciate it
To determine the maximum height of the skateboard ramp without fractions, we can start by visualizing the problem and then break it down step by step.
1. Understand the problem: We have a skateboard ramp with a width of 4 ft and a maximum angle of 45 degrees. We need to find the maximum height that can be achieved.
2. Draw a diagram: Sketch a right triangle representing the ramp, with the width as the base and the height as the perpendicular side. Label the angle of 45 degrees.
3. Use trigonometry: In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the tangent of 45 degrees gives us the relationship between the height and the width of the ramp:
tan(45°) = height / width
4. Solve for the height: Rearrange the equation to solve for the height:
height = tan(45°) * width
5. Substitute the given values: Plug in the known values of width (4 ft) and the tangent of 45 degrees:
height = tan(45°) * 4
6. Calculate the height: Use a scientific calculator or online tool to find the tangent of 45 degrees and multiply it by 4:
height ≈ 1 * 4
height ≈ 4 ft
The maximum height you should build the ramp to avoid fractions is 4 ft.