Question

An architect is designing a ramp that allows handicapped persons to get to a door's level that is 12 feet off the ground. What is the maximum angle of elevation for the rap, rounded to the nearest hundredth of a degree? What is the shortest possible length of the ramp, rounded to the nearest tenth of a foot? The ramp can not have an incline surpassing a ratio of 1:12.

Answer 1

4.780 °

144''

Explanation:

Given that,

door's level is 12 feet off the ground

the ramp can not have an incline surpassing a ratio of 1:12

An incline surpassing a ratio of 1:12 , means that every 1" of vertical rise requires at least 12" of ramp length

So,

1' rise = 12' length

12' = 12'x12

= 144''

now we know the length and height of ramp so we can use trigonometry identities to find the angle

sinФ = height / length

sinФ = 12 / 144

sinФ = sin^-1(12/144)

Ф = 4.780 °