Question

You are driving up a long inclined road. After 1.7 miles you notice that signs along the roadside indicate that your elevation has increased by 530 ft. (a) What is the angle of the road above the horizontal? (b) How far do you have to drive to gain an additional 150 ft of elevation?

Answer 1

Answer:

It’s θ = 3.38 degrees   r = 0.48mi

Explanation:

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Answer 2

Answer:

θ = 3.38 degrees

r = 0.48mi

Explanation:

a) Start by converting 1.7 mi into feet.

1mile = 5280 feet,

so 1.7 mi = 8976 ft

$y=rsin\theta,$

so $\theta = sin^{1] {530}{8976}$

and θ = 3.38 degrees

b )Now to gain another 150 ft of elevation, again use the

equation y=rsin(θ)

150 = rsin(3.38)

r = 2544.187 ft.

Convert r = 2544.187 ft into miles by dividing by 5280,

and r = 0.48mi