Chapter 11.6, Problem 6WE

To determine

To find: the missing length correct to the nearest hundred in the given triangle.

Answer to Problem 6WE

  $c=17.888$ .

Explanation of Solution

Given:

  $a=16,b=8,c=?$ .

The given triangle is shown below:

  

Calculation:

As the given triangle is right angle tringle.

Therefore, by using Pythagoras theorem, $a=16,b=8,c=?$

Thus,

  $\begin{array}{l}{c}^2=a^2+b^2\\ ={16}^2+8^2\left\{\text{substitutes the given value}\right\}\\ =256+64\{\because {16}^2=256,8^2=64\}\\ =320\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{320}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=17.888543\\ c=17.888\left\{\text{round}\text{up}\text{to}\text{nearest hundred}\right\}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=17.888$ .