Basic Problem Solving Example 2

Lesson 2: Pythagorean Theorem Problem Solving - Basic Problem Solving Example 2

   Multimedia

A video describing how to solve a basic Pythagorean Theorem word problem is provided.

EXAMPLE 2

---

Mike is replacing the roof trusses on a house. The entire span of the bottom chord is 500 inches, and the angled chord to the roof peak is 270 inches. What is the height, a, of the truss?

Solution

Step 1: Identify the given and the required values.

• The base is half of 500 inches, 250 inches.
• The hypotenuse is 270 inches.
• The height, a, is unknown

Step 2: Draw and label the diagram



Steps 3 and 4: Write the formula, substitute known values, and solve

\(\begin{align} a^2+b^2&=c^2 \\ \\ a^2+250^2&=270^2 \\ \\ a^2+62\,500&=72\,900 \\ \\ a^2+\cancel{62\,500-{\color{red}{62\,500}}}&=72\,900-{\color{red}{62\,500}} \\ \\ a^2&=10\,400 \\ \\ \sqrt{a^2}&=\sqrt{10\,400} \\ \\ a&=102 \\ \end{align}\)

The height of the truss is approximately 102 inches.

Step 5: Review the answer

The height of the truss is shorter than the hypotenuse, so the answer is reasonable.




2014 © Alberta Distance Learning Centre