Chapter 11.6, Problem 8WE

To determine

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

Answer to Problem 8WE

  $a=12.922$ .

Explanation of Solution

Given:

  $a=?,b=11,c=17$ .

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,

  $\begin{array}{l}{c}^2=a^2+b^2\\ \Rightarrow a^2=c^2-b^2\\ ={17}^2-1^2\left\{\text{substitutes the given value}\right\}\\ =289-121\{\because {11}^2=121,{17}^2=289\}\\ =167\left\{\text{subtract the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore a=\sqrt{167}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow a=12.922\{\text{simplify}}\\ a=12.922\left\{\text{round up to nearest hundredth}\right\}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $a=12.922$ .