4-2: Finding Unknown Leg Lengths

Key Concept

You used the Pythagorean Theorem to find the hypotenuse of a right triangle when you knew the lengths of the legs. You can also use the Pythagorean Theorem to find the length of a leg when you know the hypotenuse and the length of the other leg.

A right triangle with legs a and b and hypotenuse c.

Part 1

Example Calculating Unknown Leg Lengths Using the Pythagorean Theorem

What is the length of the unknown leg in each triangle?

  • a. A right triangle with a leg of length 12 m and a hypotenuse of length 13 m.

  • b. A right triangle with a leg of length 9 m and a hypotenuse of length 15 m.

  • c. A right triangle with a leg of length 10.5 m and a hypotenuse of length 17.5 m.

  • d. A right triangle with a leg of length 15 m and a hypotenuse of length 25 m.

Solution

For each triangle, substitute the known values into the Pythagorean Theorem. Then solve the equation to find the length of the unknown leg.

  • a. A right triangle with a hypotenuse of length 13 m, a leg of length 12 m, and another leg labeled a. Let a represent the length of the unknown leg.


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Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties