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3 years ago

15

You want to build a wheelchair ramp leading up to your house. Your front door is 2 feet higher than the driveway and you would l

ike the grade of the ramp to be 7%. (a) What is the angle, θ, that the ramp forms with the driveway? (Round your answer to three decimal places.) s ° (b) How long does the driveway have to be to build this ramp? (Round your answer to two decimal places.) s ft (c) How long will the ramp be? (Round your answer to two decimal places.)

1 answer:

Alenkasestr [34]3 years ago

4 0

Answer: (a) The angle the ramp forms with the driveway, s° = 4.004° (3 d.p)

(b) The driveway has to be, s = 28.57 ft

(c) The ramp will be 28.64 ft long

Step-by-step explanation:

First key thing to know is that the %grade of a ramp = rise/ramp run

%grade of a ramp = 7% = 0.07

(Kindly find attached a diagram to assist with understanding).

Also note that, <em>the ramp run is not the same as the ramp length</em>

(a) the angle, θ, is the angle of slope between the driveway and the ramp,

tan θ = 0.07,

θ = tan⁻¹ 0.07 = 4.004° (3 d.p)

(b) the length of the driveway (s) is the same as the length of the ramp run, so, %grade of a ramp = rise/ramp run

0.07 = 2/s

s = 2/0.07 = 28.57 ft (2 d.p)

(c) the length of the ramp can be found by using Pythagoras' theorem,

L = ramp length = $\sqrt{rise^{2} + ramprun^{2} }$

L = $\sqrt{2^{2} +28.571^{2} }$

L = $\sqrt{820.3041}$

L = 28.64 ft (2 d.p)

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