A company plans to build a wheelchair ramp with the following dimensions: the ramp is 43.5 ft long and has a vertical height of 3 ft.
Regulations state that the angle the ramp makes with the ground cannot
be greater than 4.8 degrees. Does this company's plan comply with the
regulations? Use mathematical evidence to support your claim.

9514 1404 393

  yes

Step-by-step explanation:

The height that would be allowed with a ramp 43.5 feet long is ...

  h = (43.5 ft)·sin(4.8°) ≈ 3.64 ft

The proposed height is less than 3.64 ft, so the ramp angle is less than 4.8°.

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The ramp angle is actually arcsin(3/43.5) ≈ 3.95°, which is less than 4.8°.

Circumference of a cicle in terms of radius:

Circumference = 2·π·r = 2·3.14·2.5 = 15.7(*)

In terms of diameter:

Circumference = π·d = 3.14·5 = 15.7(*)

In terms of area:

Circumference C = √4·π·A = √4·π·19.63 = 15.7(*)

Answer?→(*) 15.71

Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.