Decline in a Road

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A road declines 30° from horizontal over a distance of 60 feet, as measured by a tape on the road's surface. At the base of the incline is a hole 7 feet deep. What is the difference in elevation between the top of the incline and the bottom of the hole?

Review: Decline in a Road


Explanation

Most questions involving geometry warrant the brief effort to sketch a figure. For example, we want to be sure we capture "30 degrees from horizontal" correctly.



The triangle is a 30-60-90 triangle, because the top angle is 60 and it's a right triangle. We have the length of the side (60 feet) corresponding to the right angle, and we want to find the shortest side, the one measuring the vertical drop, which corresponds to the smallest angle, 30 degrees.



The drop is 30 feet. Adding the depth of the hole, the total drop is 37 feet.

The correct answer is (B).


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