Question

A cement company is installing a 20 -foot-long wheelchair ramp sidewalk leading to the front door of a business office. The angle of elevation of the ramp is 2. How far is the door above the normal height of the ground. (round to one decimal place)

Answer 1

To find the height of the door above the ground for a 20-foot ramp at a 2-degree angle, calculate the sine of the angle in radians, then multiply by the length of the ramp. The door is approximately 0.7 feet above the ground.

Step-by-step explanation:

To determine how far the door is above the normal height of the ground for a wheelchair ramp with a 20-foot length and a 2-degree angle of elevation, we need to use trigonometric functions. In this case, we can use the sine function (sin) which is defined as opposite/hypotenuse.

The formula to find the height (h) is:

h = length × sin(angle)

The calculation steps are as follows:

1. Convert the angle from degrees to radians: angle in radians = angle in degrees × (π / 180)
2. Calculate the sine of the angle.
3. Multiply the length of the ramp (hypotenuse) by the sine of the angle to find the height.

Using these steps, you'd perform the following calculation to find the height to one decimal place:

• angle in radians = 2 × (π / 180)
• sin(2 degrees) ≈ 0.0349
• Height h ≈ 20 × 0.0349
• h ≈ 0.698 feet

Therefore, the door is approximately 0.7 feet above the normal height of the ground.