High school or college geometry students may be asked to find the lengths of a triangle's sides. Engineers or landscapers may also need to determine the lengths of a triangle's sides. If you know some of the sides or angles of the triangle, you can figure out the unknown measurements.
Use the Pythagorean theorem for right triangles in which two sides are given. (This theorem is A^2 + B^2 = C^2. A and B are regular sides, and C is the hypotenuse.) If you're trying to find the hypotenuse, square the other sides, add them together and take the square root. If you're trying to find a side other than the hypotenuse, square the side given, subtract it from the hypotenuse squared, and take the square root of the answer.
Recognize that an equilateral triangle has three equal sides. Therefore, if one side is given, the other two are the same measurement.
Recognize that an isosceles triangle has two equal sides and two equal angles. Therefore, if the length of one of the equal sides is unknown, you can deduce that the other side is the same length as the similar side given.
- Side or angle measurements
Begin using the law of cosines by multiplying the squares of two given sides. The product you get will be needed in a later step.
Multiply the two given sides. (Do not square them.)
Multiply the answer from step 2 by 2.
Multiply the answer from step 3 by the cosine of the angle opposite the unknown sides. (Use a calculator with trigonometry functions to find the cosine of this angle.)
Subtract the answer from step 4 from the answer you obtained in step 1.
Take the square root of the answer from step 5 to find the measurement of the unknown side.
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