Chapter 8, Problem 16CT

To determine

The value of x in the given triangle

Answer to Problem 16CT

The value of x is $\sqrt{3}$

Explanation of Solution

Given information: An isosceles triangle with two angles equal to 45⁰ and one side being $\sqrt{6}$ units.

Formula Used:

1) The sum of angles in a triangle is 180⁰.

2) The relationship between the legs of right triangle (shown in figure below) a , b and its hypotenuse c is obtained by using Pythagoras theorem.

  

It can be expressed as,

  $\begin{array}{l}{c}^2=a^2+b^2\\ c=\sqrt{a^2+b^2}\end{array}$

Calculation:

Here, the two of the angles in the triangle is given as 45⁰. Therefore, the third angle which is opposite to the side of measure $\sqrt{6}$ units is given by,

  $\begin{array}{c}A=180°-\left(45°+45°\right)\\ =90°\end{array}$

Thus, the given triangle is a right triangle. So, applying Pythagoras theorem gives,

  

  $\begin{array}{c}\sqrt{6}=\sqrt{x^2+x^2}\\ =x\sqrt{2}\\ x=\frac{\sqrt{6}}{\sqrt{2}}\\ =\sqrt{3}\end{array}$