Chapter 11.6, Problem 3WE

To determine

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

Answer to Problem 3WE

  $c=9.433$ .

Explanation of Solution

Given:

  $a=8,b=5,c=?$ .

The given triangle is shown below:

  

Calculation:

As the given triangle is right angle tringle.

Therefore, by using Pythagoras theorem, $c^2=a^2+b^2$

Thus,

  $\begin{array}{l}{c}^2=a^2+b^2\\ =8^2+5^2\left\{\text{substitutes the given value}\right\}\\ =64+25\{\because 8^2=64,5^2=25\}\\ =89\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{89}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=9.4339\\ c=9.433\left\{\text{round}\text{up}\text{to}\text{nearest hundred}\right\}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=9.433$ .