Question

a ramp is used to provide access to the entrance of a store. the length of the ramp is 20 feet. the angle of elevation that the ramp makes with the ground is 4.8°. what is the height of the ramp, rounded to the nearest tenth of a foot, at the entrance of the store? enter your answer in the box. your answer must be rounded to the nearest tenth. feet

Explanation:

Step1: Identify trigonometric relation

The ramp, ground, and height form a right triangle. The ramp is the hypotenuse (\(c = 20\) ft), the height (\(h\)) is the opposite side to the angle of elevation (\(\theta = 4.8^\circ\)). We use \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(4.8^\circ)=\frac{h}{20}\).

Step2: Solve for height

Rearrange the formula: \(h = 20\times\sin(4.8^\circ)\). Calculate \(\sin(4.8^\circ)\) (in degree mode). \(\sin(4.8^\circ)\approx0.0837\). Then \(h = 20\times0.0837 = 1.674\). Round to nearest tenth: \(h\approx1.7\).

Answer:

1.7