Question

billy is building a ramp. the ramp creates a 12 degree angle with the ground and is 32 feet from the building. the ramp is ___ feet long. (round to the nearest tenth)

Answer 1

The ramp is 32.7 feet long

Explanation:

The geometrical conditions of the question are shown in the figure below.

Let L be the length of the ramp. The ramp, the wall of the building, and the ground form a right triangle where L is its hypotenuse and the distance of 32 ft is the adjacent leg to the angle of 12°.

To find the length of the hypotenuse, we use the trigonometric ratio called the cosine:

`\displaystyle \cos\beta=\frac{\text{adjacent leg}}{\text{hypotenuse}}`

`\displaystyle \cos12^\circ=(32)/(L)`

To find L, we solve the above equation:

`\displaystyle L=(32)/(\cos12^\circ)`

The cosine of 12° is computed with a scientific calculator:

`\displaystyle L=(32)/(0.978)`

L = 32.7 feet

The ramp is 32.7 feet long