Question

Trigonometric classmate

Prompt: You are purchasing a large slab of wood to build a wheelchair ramp for your classmate to make it easier for her to get to her classes. You have to make sure that the ramp is 20 degrees from the ground so that it is not too steep.
The base of the ramp should be about 5 feet away from the top of the step.
How many feet long should the slab of wood be? Use right triangle trigonometric ratios to help you answer this question. round vour answer to the nearest whole number. (40 points)
Explain your process for solving this problem. (60 points) (Hint: Make sure your calculator is in degree mode.)

Please help me!!

Answer 1

To find the length of the ramp, we can use the tangent ratio in a right triangle. By substituting the known values into the equation, we can calculate the height of the ramp. The slab of wood should be approximately 1.82 feet long.

Step-by-step explanation:

To solve this problem, we can use trigonometry and the right triangle formed by the ramp. We know that the angle between the ground and the ramp is 20 degrees, and the base of the ramp is 5 feet away from the top of the step. We can use the tangent ratio to find the length of the ramp. The tangent of an angle is equal to the opposite side divided by the adjacent side.

1. First, we label the sides of the right triangle. The side opposite the angle of 20 degrees is the height of the ramp (h), and the side adjacent to the angle is the base of the ramp (b).
2. We know that the tangent of 20 degrees is equal to the height of the ramp divided by the base of the ramp. So, we can write the equation: tan(20) = h / 5.
3. We can rearrange the equation to solve for the height of the ramp: h = 5 * tan(20).
4. Now, we can calculate the height of the ramp by substituting the value of tangent(20) from a calculator. On a calculator in degree mode, the tangent of 20 degrees is approximately 0.364.
5. Using this value, we can find the height of the ramp: h = 5 * 0.364 = 1.82 feet (rounded to the nearest whole number).

Therefore, the slab of wood should be approximately 1.82 feet long.

Answer 2

Check the picture below.

`\cos(20^o)=\cfrac{\stackrel{adjacent}{x}}{\underset{hypotenuse}{5}}\implies 5\cos(20^o)=x\implies 5\approx x`

Make sure your calculator is in Degree mode.