a wheelchair ramp must rise 32 in. to meet the door of a courthouse. if the ramps angle of elevation is not to exceed 4.1 degrees, whats the minimum horizontal length of the ramp? (nearest foot)

Answer 1

a wheelchair ramp must rise 32 in. to meet the door of a courthouse. if the ramps angle of elevation is not to exceed 4.1 degrees, whats the minimum horizontal length of the ramp? (nearest foot)

We have a right triangle with the angle of elevation ≤4.1° and a height of 32 inches. So the right triangle's leg opposite the elevation angle is 32"

Let's set Ø=angle of elevation ≤ 4.1°

If X is the horizontal length,

tanØ=32/X

X/32=cotØ

X≥32cot(4.1)

X≥437 inches

Answer 2

tan 4.1 = 32/x

x = 32 / tan 4.1

x=446.423

37 feet 2 and 7/16 inches

Answer 3

You are given the opposite side and are looking for the adjacent side. Therefore, you can use tangent to solve this one.

tan Θ = opposite/adjacent plug in what is given

tan 4.1 = 32/x multiply both sides by x

x tan 4.1 = (32/x)(x) Simplify

x tan 4.1 =32 Divide both sides by tan 4.1

x tan 4.1/tan 4.1 = 32/tan 4.1 Simplify

x = = 32/tan 4.1 Make sure calculator is in degrees and not radians

x = 446.4 in/12 inches/ft

x = 37 ft