1Cademy - Finding a Leg of an 8-15-17 Right Triangle

Learn Before

Finding a Leg of a 5-12-13 Right Triangle

Example

Finding a Leg of an 8-15-17 Right Triangle

Apply the Pythagorean Theorem and the geometry problem-solving strategy to find an unknown leg of a right triangle when one leg and the hypotenuse are given.

Problem: Use the Pythagorean Theorem to find the length of the unknown leg in a right triangle with one leg measuring $15$ units and a hypotenuse measuring $17$ units.

Read the problem and visualize the figure.
Identify what you are looking for: the length of the unknown leg.
Name: Let $b$ be the length of the unknown leg. Label the triangle components with the leg as $15$ units and the hypotenuse as $17$ units.
Translate: Write the Pythagorean Theorem formula and substitute the known measures: $a^2 + b^2 = c^2$ giving $15^2 + b^2 = 17^2$ .
Solve the equation. Evaluate the numerical squares: $225 + b^2 = 289$ . Isolate the squared variable by subtracting $225$ from both sides: $b^2 = 64$ . Use the definition of the square root (retaining solely the positive root for physical length features): $b = \sqrt{64}$ giving $b = 8$ .
Check the result: Does $15^2 + 8^2 = 17^2$ ? $225 + 64 = 289$ , meaning $289 = 289$ $\checkmark$ .
Answer: The length of the leg is $8$ units.

Updated 2026-05-02

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn Before

Related