Question

Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the ground to the floor of the porch, which is 2 1/2

ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.

What length board should Jessica buy if she uses the maximum angle of incline?

Enter your answer in the box. Round only your final answer to the nearest tenth.

Answer 1

The board must be about 4.4 ft long

Answer 2

Length of board should Jessica buy is 4.4 feets.

Explanation:

Height of the ramp =
`2(1)/(2) ft=(5)/(2) ft`

Distance of the porch from the ground = x

Inclination of the ramp,θ = 35°

In triangle ABC,

AB =
`(5)/(2) ft`

AC = x

θ = 35°

According trigonometric ratios:

`\sin \theta =(Perpendicular)/(hypotenuse)`

`\sin 35^o =(AB)/(AC)`

`0.573576=((5)/(2) ft)/(x)`

`x=4.3586 ft\approx 4.4 ft`

Length of board should Jessica buy is 4.4 feets.