Lesson 3: Solving Problems using Trigonometry - Getting Into It

   Getting Into It

Here is what you will need for the following investigation:

  • calculator
  • pencil and paper

Recall from Chapter 3 that for a right triangle with legs a and b, and hypotenuse c, a2 + b2 = c2. This relationship is the Pythagorean theorem or Pythagoras' theorem.

The Pythagorean theorem can be used to determine the length of an unknown side of a right triangle when two of the side lengths are known.

Task


Review the Pythagorean theorem by solving for the unknown side length.

A right triangle has a hypotenuse length of 15 m and a leg length of 12 m. Determine the length of the triangle's other leg.

Solution


\(\begin{align} a^2+b^2&=c^2 \\ \\ \left(12\,\text{m}\right)^2+b^2&=\left(15\,\text{m}\right)^2 \\ \\ 144\,\text{m}^2+b^2&=225\,\text{m}^2 \\ \\ b^2&=225\,\text{m}^2-144\,\text{m}^2 \\ \\ b^2&=81\,\text{m}^2 \\ \\ \sqrt{b^2}&=\sqrt{81\,\text{m}^2} \\ \\ b&=9\,\text{m} \\ \end{align}\)

The length of the other leg is 9 m.


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