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Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.40 · Physics Playground

Exercises Word problems and geometry

Example 3.40 from Elementary Algebra, 3.4 Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem

Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.40

Use the Pythagorean Theorem to find the length of the leg shown below.

A right angle with one leg marked 5. The hypotenuse is labeled 13.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Step 1. Read the problem.
Step 2. Identify what you are looking for.		the length of the leg of the triangle
Step 3. Name. Choose a variable to represent it.		Let b = the leg of the triangle.
Lable side b.
Step 4. Translate
Write the appropriate formula.		$a^{2} + b^{2} = c^{2}$
Substitute.		$5^{2} + b^{2} = 13^{2}$
Step 5. Solve the equation.		$25 + b^{2} = 169$
Isolate the variable term.		$b^{2} = 144$
Use the definition of square root.		$b^{2} = \sqrt{144}$
Simplify.		$b = 12$
Step 6. Check.
Step 7. Answer the question.		The length of the leg is 12.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

A right triangle with legs marked b and 15. The hypotenuse is marked 17.

How did it go?

PreviousSolve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.39 Next Solve Geometry Applications: Triangles, Rectangles, and the Pythagorean Theorem: example 3.41

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 3.4, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.