Chapter 11.6, Problem 46E

To determine

To calculate: the unknown length of the triangle.

Answer to Problem 46E

the unknown length of the triangle is $8in.$ .

Explanation of Solution

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

  $\begin{array}{l}\text{hypotenuse c=10in}\text{.}\\ \text{side of the right angle a=6in}\end{array}$

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.

  $a^2+b^2=c^2$

  $a=6$

  $c=10$

  $\begin{array}{l}{\left(6\right)}^2+{\left(b\right)}^2={\left(10\right)}^2\text{ [substitue a by 6 and c by 10]}\\ 36+{\left(b\right)}^2=100\text{ [square]}\\ b^2=100-36\text{ [subtract]}\\ b=8\text{ [square root]}\end{array}$

Hence,the unknown length of the triangle is $8in.$ .