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How to Measure the Distance between Two Rooftops

Trigonometry functions have everyday applications. You can use a trig function to measure the distance between two rooftops — you just have to be standing on one of them.

Here’s an example: Jumping Jehoshaphat makes his living by jumping, on his motorcycle, from building to building, cliff to bluff, or any place he can get attention for doing it. His record jump is a distance of 260 feet, from one building to another. Jehoshaphat is on to his next feat and needs to determine the distance from one building to another.

image0.jpg

His assistant, Lovely Lindsay, holds a 6-foot pole perpendicular to the roof she’s standing on. The two buildings are exactly the same height. When Jehoshaphat, standing on top of the first building, sights straight across to a point at the base of the pole and then sights a point halfway up the pole, the angle of elevation is 1 degree. Will he be able to make the jump? See the preceding figure for a visual of Jehoshaphat’s calculation.

  1. Identify the parts of the right triangle that you can use to solve the problem.

    You know the value for the side opposite the 1-degree angle, which is half the pole length, and the adjacent side is the unknown distance. Call that distance x.

  2. Determine which trig function to use.

    The tangent of an angle uses opposite divided by adjacent.

  3. Write an equation with the trig function, then input the values that you know.

    The length of half the pole is 3 feet, so the equation looks like this:

    image1.png
  4. Solve for the value of x.

    Use a scientific calculator to find the value of the tangent of 1 degree.

    image2.png

    You find that the distance between the buildings is a little less than 172 feet across. Jehoshaphat should be able to make the jump easily, because his record is 260 feet.

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