Chapter 11.6, Problem 7WE

To determine

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

Answer to Problem 7WE

  $a=20$ .

Explanation of Solution

Given:

  $a=?,b=21,c=29$ .

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,

  $\begin{array}{l}{c}^2=a^2+b^2\\ \Rightarrow a^2=c^2-b^2\\ ={29}^2-{21}^2\left\{\text{substitutes the given value}\right\}\\ =841-441\{\because {21}^2=441,{29}^2=841\}\\ =400\left\{\text{subtract the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore a=\sqrt{400}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow a=\sqrt{{20}^2}\{\text{simplify}}\\ a=20\{\sqrt{a^2}=a\}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $a=20$ .