Amanda wants to shorten the wheelchair ramp at her front door. The current
ramp is 13 feet along the horizontal and the step is 9 inches high. If she doubles
the measure of the angle that the ramp makes with the walkway, how long will the new ramp be to the nearest inch?
Right now, rise/run = 9/156
so tanØ = 9/156
Ø = 3.302°
So she wants the angle to be 6.604°
Then, assuming the rise will remain the same,
tan 6.604° = 9/length
length = 9/tan6.604 = 77.7 inches or
78 inches
To find the length of the new ramp, we can use trigonometry. Let's break down the problem and find a solution:
1. Given information:
- The current ramp is 13 feet along the horizontal.
- The step is 9 inches high.
- Amanda wants to double the measure of the angle that the ramp makes with the walkway.
2. We need to determine the length of the new ramp. Let's call it "x".
3. We can use the trigonometric function tangent (tan) to relate the angle with the ratio of the opposite (9 inches) to the adjacent (x feet) sides of a right triangle. The tangent function is defined as:
tan(angle) = opposite / adjacent
tan(angle) = 9 inches / x feet
4. Because we want to double the angle, we can define the new angle as "2 * angle". So, the new equation becomes:
tan(2 * angle) = 9 inches / x feet
5. Rearranging the equation to solve for "x", we get:
x feet = 9 inches / tan(2 * angle)
6. To find the new length in feet, we need to convert inches to feet. Since there are 12 inches in a foot, we divide the inches by 12:
x feet = (9 inches / 12) / tan(2 * angle)
x feet = 0.75 feet / tan(2 * angle)
7. Finally, we need to convert the length in feet to the nearest inch. We can do this by rounding the value to the nearest whole number.
Now you can use a calculator to find the value of "x" by plugging in the value of "2 * angle".