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Chapter 10: Problem 83

A straight road rises with an inclination of 0.10 radian from the horizontal (see figure). Find the slope of the road and the change in elevation over a two-mile stretch of the road.

Short Answer

Expert verified
The slope of the road would be the tangent of 0.10 radian. The change in elevation over a 2-mile stretch would be the product of this slope and the horizontal distance of 2 miles.

Step by step solution

01

Converting Radian Measure to Slope

The slope of a line, in math, is a measure of how steep the line is. Within the context of trigonometry, the slope is equivalent to the tangent of the angle of inclination. In this case, the inclination is 0.10 radians. Hence, the slope of the road can be calculated as the tangent of the given radian measure, which is \( \tan(0.10) \).
02

Calculate Change in Elevation

With the slope (as calculated in step 1) and given horizontal distance of 2 miles (or any other unit), we can find the change in elevation. The change in elevation is simply the product of the slope and the horizontal distance (since change in height = slope 脳 horizontal distance). Hence, to calculate the change in elevation over a two-mile stretch of the road, multiply the slope by the horizontal distance of 2 miles.

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