Use the Law of Cosines with a Triangle
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Find the Area of a Triangle Using ASA

How to Find the Distance across a Pond

Trigonometry is very handy for finding distances that you can’t reach to measure. Imagine that you want to string a cable diagonally across a pond (so you can attach a bunch of fishing line and hooks). The diagonal distance is the hypotenuse of a right triangle. You can measure the other two sides along the shore.

The figure shows the pond and the imaginary right triangle you use to figure out how long your cable needs to be.


The two sides of the triangle that you can measure, the height and the width of the pond, are 40 feet and 96 feet. These are the two legs of a right triangle. Use the Pythagorean theorem to solve for the hypotenuse, which is the diagonal distance across the pond.

  1. Replace the variables in the theorem with the values of the known sides.

    402 + 962 = c2

  2. Square the measures, and add them together.

  3. Find the square root of the sum.


The diagonal across the pond is 104 feet. String up your cable, and go fishing!

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