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A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles. To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section?
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A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles.

To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance.

User Michael Glukhovsky
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1 Answer

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1) Draw a right triangle with these measures:

angle with the horizontal: 6 degress
horizontal segment: 5
height: x

2) Definition of tangent : tan(6°) = opposite leg / adjacent leg = x / 5 =>

3) Solve for

x = 5tan(6°) = 0.53 miles

Answer: 0.53 miles
User Yvonne Aburrow
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