Chapter 11.6, Problem 47E

To determine

To calculate: the unknown length of the triangle.

Answer to Problem 47E

the unknown length of the triangle is $\sqrt{21}ft$ .

Explanation of Solution

Given : from the figure provided in the question it is observed that,

  $\begin{array}{l}\text{hypotenuse c=5feet}\text{.}\\ \text{side of the right angle b=2feet}\end{array}$

Formula used: Pythagorean theorem,

  $\begin{array}{l}{a}^2+b^2=c^2\\ a=\text{side of right angle}\\ \text{b=side of right angle}\\ \text{c=hypotenuse}\end{array}$

Calculation : tofind the unknown length we use the Pythagorean theorem, and put the values in the above formula.

  $a^2=b^2+c^2$

  $b=2$

  $c=5$

  $\begin{array}{l}{\left(2\right)}^2+{\left(a\right)}^2={\left(5\right)}^2\text{ [substitue b by 2 and c by 5]}\\ 4+a^2=25\text{ [square]}\\ a^2=21\text{ [subtract]}\\ a=\sqrt{21}\text{ [square root]}\end{array}$

Hence,the unknown length of the triangle is $\sqrt{21}ft$ .