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How Do You Find the Length of a Leg of a Right Triangle?

Find the length of the missing side of the given triangle.

Summary

  1. The triangle's hypotenuse has a length of 20, and one leg has a length of 8
  2. The small box in the corner of the triangle represents a 90-degree, or right angle
  3. Since we have a right triangle, we can use the Pythagorean Theorem to solve for the missing length
  4. 'a', 'b', and 'c' represent the three sides of the triangle, where 'a' and 'b' are the legs and 'c' is the hypotenuse
  5. The symbols over the b2 and 336 are square roots
  6. Taking the square root of a squared number will get rid of the square
  7. The ≈ symbol means 'is approximately equal to'

Notes

    1. 'a' and 'b' are the lengths of the legs: the two shorter sides of the right triangle
    2. 'c' is the length of the hypotenuse: the longest side of the right triangle
    3. Since we have a right triangle, we can use the Pythagorean Theorem to solve for the missing length
    1. Since we have a right triangle, we want to identify 'a', 'b', and 'c' and plug them into the Pythagorean Theorem
    2. 'a' and 'b' are the lengths of the legs: the two shorter sides of the right triangle
    3. 'c' is the length of the hypotenuse: the longest side of the right triangle
    1. The legs are the two shorter sides that come together to form the right angle
    2. It doesn't matter which leg we pick to be 'a' and which to be 'b'
    1. The hypotenuse is always across from the right angle in a right triangle
    1. We can plug 8 in for 'a' and 20 in for 'c' into the Pythagorean Theorem
    2. So we get 82 + b2 = 202
    1. Squaring 8 gives us 64 and squaring 20 gives us 400
    2. Subtracting 64 from both sides of 64 + b2 = 400 will get b2 by itself on the left side: b2 = 336
    1. Taking the square root of a squared number gets rid of the squared part
    2. The symbols over the b2 and 336 are square roots
    3. So the square root of b2 is just 'b'
    1. Since 336 = 16•21, √(336) = √(16•21)
    2. The Product Property of Square Roots lets us break √(16•21) into √(16)•√(21)
    3. Then we can simplify √(16) to 4 and rewrite √(336) as 4√(21)
    4. The √ symbols represent square roots
    1. 4 times the square root of 21 is the most exact answer we can get for the length of 'b'
    2. The ≈ symbol means 'is approximately equal to'