Question

What must the angle of elevation of the ramp be for the ramp to be 15 feet long and reach the front door that is 3 feet high?

a) 11 degrees
b) 12 degrees
c) 13 degrees
d) 14 degrees

Answer 1

Using the sine function, the angle of elevation for a 15-foot ramp to reach a height of 3 feet is approximately 11.54 degrees. The closest given option is 11 degrees.

Step-by-step explanation:

To find the angle of elevation that a 15 feet long ramp makes with the ground to reach a height of 3 feet, we use trigonometry. Since we have the opposite side (height) and the hypotenuse (length of the ramp), we can use the sine function. The sine of the angle θ is equal to the opposite side divided by the hypotenuse.

Using the sine formula:

sin(θ) = opposite / hypotenuse

sin(θ) = 3 feet / 15 feet

sin(θ) = 0.2

Now, we take the inverse sine (arcsine) to solve for θ:

θ = arcsin(0.2)

θ ≈ 11.54 degrees

The closest answer to this is option (a), which states 11 degrees.