Chapter 9, Problem 16CT

To determine

Tofind:The unknown length

Answer to Problem 16CT

  $a=2\sqrt{41}$

Explanation of Solution

Given information:

Formula used:

Pythagoras Theorem- $a^2+b^2=c^2$

Where $a$ and $b$ are legs of right angled triangle and $c$ is hypotenuse

Calculation:

In the given triangle-

  $\begin{array}{l}{a}^2+b^2=c^2\\ \Rightarrow a^2+{\left(14\right)}^2={\left(20\right)}^2\\ \Rightarrow a^2+196=400\\ \Rightarrow a^2=400-196\\ \Rightarrow a^2=204\\ \Rightarrow a=\sqrt{204}\\ \Rightarrow a=\sqrt{4·41}\\ \Rightarrow a=2\sqrt{41}\end{array}$