Question

If a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 13 feet long, what angle does the ramp make with the ground extending from the ramp to the truck? (Round your answer to one decimal place.)

Answer 1

The angle that the ramp makes with the ground extending from the ramp to the truck is approximately 17.5 degrees.

Step-by-step explanation:

We can start by drawing a right triangle where the hypotenuse is the ramp, the height is 4 feet, and the base is the distance from the truck to the bottom of the ramp (the horizontal distance).

Since we know the length of the hypotenuse and the height of the triangle, we can use the sine function to find the measure of the angle:

sin(θ) = opposite/hypotenuse

sin(θ) = 4/13

Now, we can solve for θ by taking the inverse sine (sin^-1) of both sides:

θ = sin^-1(4/13)

Using a calculator, we get:

θ ≈ 17.5 degrees