Question

a ramp is attached to a movers truck. the ramp is 8 ft long and the truck box is 5 ft off the ground.
a diagram of the ramp with dimensions is below.

1. to the nearest degree, determine the angle that the ramp makes with the ground.

hint: \\( \theta = \\)
opposite =
adjacent =
trig ratio used:
remember you will need to use your inverse function on your calculator to find the angle.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine ratio is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the angle \(x\) is the angle between the ramp (hypotenuse, \(h = 8\) ft) and the ground. The side opposite to the angle \(x\) is the height of the truck box (\(a=5\) ft). So, \(\sin x=\frac{5}{8}\).

Step2: Solve for the angle \(x\)

We use the inverse sine function \(x = \sin^{-1}(\frac{5}{8})\).
Using a calculator, \(\sin^{-1}(\frac{5}{8})\approx39^{\circ}\) (rounded to the nearest degree).

Answer:

The angle that the ramp makes with the ground is approximately \(39^{\circ}\).