Lesson 2: Pythagorean Theorem Problem Solving - Basic Problem Solving

   Constructing Knowledge

The following steps can be followed when solving word problems involving right triangles.

  1. Identify the given and the required values.
  2. Draw a diagram if one isn't provided. Label the diagram with the given information.
  3. Write the formula using the information labelled on the diagram.
  4. Solve for the unknown.
  5. Review the answer to ensure it makes sense. (Always verify that the hypotenuse is the longest side).

A proper diagram is key. If you are unsure if your diagram is correct, contact your teacher.

Questions will typically involve a right triangle as part of the diagram unless you are being asked to determine if the triangle has a right angle.

EXAMPLE 1

A guy wire is attached to a power pole 20 feet above the ground. It is attached to the ground 5 feet from the base of the power pole. How long is the guy wire?

Solution


Step 1: Identify the given and the required values.

  • The height is 20 feet.
  • The base is 5 feet.
  • The length of the hypotenuse (wire) is unknown.

Step 2: Draw and label the diagram.



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

\(\begin{align} h^2+b^2&=w^2 \\ \\ 20^2+5^2&=w^2 \\ \\ 400+25&=w^2 \\ \\ 425&=w^2 \\ \\ \sqrt{425}&=\sqrt{w^2} \\ \\ 20.6&=w \\ \end{align}\)

The guy wire is approximately 20.6 feet long.

Step 5: Review the answer.

The guy wire is the hypotenuse, and it is the longest side of the triangle. As such, the answer is reasonable.


Now, it is your turn! Complete the questions in your Chapter 3, Lesson 2 Practice Makes Perfect that refer to Basic Problem Solving.



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