Chapter 11.6, Problem 45E

To determine

To calculate: the unknown length of the triangle.

Answer to Problem 45E

the unknown length of the triangle is $52m$ .

Explanation of Solution

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

Side of right triangle $a=20m$ .

Side of right triangle $b=48m$

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.

  $a^2+b^2=c^2$

  $a=20$

  $b=48$

  $\begin{array}{l}{\left(20\right)}^2+{\left(48\right)}^2=c^2\text{ [substitue a by 20 and b by 48]}\\ 400+2304=c^2\text{ [square]}\\ c^2=2704\text{ [add]}\\ c=52\text{ [square root]}\end{array}$

Hence,the unknown length of the triangle is $52m$ .