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

Answer:

Length of board should Jessica buy is 4.4 feets.

Step-by-step explanation:

Height of the ramp = $2\frac{1}{2} ft=\frac{5}{2} ft$

Distance of the porch from the ground = x

Inclination of the ramp,θ = 35°

In triangle ABC,

AB = $\frac{5}{2} ft$

AC = x

θ = 35°

According trigonometric ratios:

$\sin \theta =\frac{Perpendicular}{hypotenuse}$

$\sin 35^o =\frac{AB}{AC}$

$0.573576=\frac{\frac{5}{2} ft}{x}$

$x=4.3586 ft\approx 4.4 ft$

Length of board should Jessica buy is 4.4 feets.