Chapter 11.6, Problem 25WE

To determine

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

Answer to Problem 25WE

  $c=25.612$ .

Explanation of Solution

Given:

  $a=\frac{4}{5}b,b=20,c=?$ .

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,

  $\begin{array}{l}{c}^2=a^2+b^2\\ ={20}^2+{16}^2\{b=20,a=\frac{4}{5}\times 20=16\}\\ =256+400\{\because {16}^2=256,{20}^2=400\}\\ =656\left\{\text{add the both terms}\right\}\end{array}$

  $\begin{array}{l}\therefore c=\sqrt{256}\left\{\text{taking square root on both the sides}\right\}\\ \Rightarrow c=25.612\{\text{up to nearest hundred}}\end{array}$

Hence, the missing length correct to the nearest tenth in the given triangle is $c=25.612$ .