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You are driving up a long, inclined road. After 1.50mi you notice that signs along the roadside indicate that your elevation has increased by 510ft . b) How far do you have to drive to gain an additional 110ft of elevation

Sagot :

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Answer:

1.825 miles

Explanation:

Given that :

Distance driven = hypotenus = 1.5 miles

Elevation at distance of 1.5 miles = 510 feets

Converting miles to feets for the hypotenus :

1 mile = 5280 feets

1.5 miles = (5280 * 1.5) = 7920 feets

To obtain the angle of inclination :

Using Pythagoras rule :

Sinθ = opposite / hypotenus

θ = Sin^-1(510 / 7920)

θ = 3.692°

For an additional elevation of 110 ft ; new height = 110 + 510 = 620 feets

Distance driven, d =?

Sin 3.69 = (620 / d)

0.0643581 * d = 620

d = 620 / 0.0643581

d = 9633.5970 feets

Converting to feets :

9633.5970 / 5280 = 1.8245448

= 1.825 miles

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