Chapter 11, Problem 12CT

To determine

To find: The length of the other side to the nearest hundredth.

Answer to Problem 12CT

The length of other side is approx $\text{17}\text{.23}\text{}\text{m}$ .

Explanation of Solution

Given information:

The length of hypotenuse is $19\text{m}$ .

The length of one of the shorter side is $8\text{}\text{m}$ .

Calculation:

Use Pythagorean theorem.

  ${\text{hypotenuse}}^{\text{2}}={\text{base}}^{\text{2}}+{\text{height}}^{\text{2}}$

Substitute the value in above formula.

  $\begin{array}{l}{\left(19\text{}\text{m}\right)}^2={\left(8\text{}\text{m}\right)}^2+{\left(\text{height}\right)}^2\\ {\left(\text{height}\right)}^2={\left(19\text{}\text{m}\right)}^2-{\left(8\text{}\text{m}\right)}^2\\ \text{height}=\sqrt{361-64}\\ \text{height}\approx \text{17}\text{.23}\end{array}$

  $\frac{1}{2}\left(\sqrt{2n}\right)=5$

Therefore, the length of other side is approx $\text{17}\text{.23}\text{}\text{m}$ .