Chapter 4.4, Problem 4WE

To determine

Value of x in the given figure.

Answer to Problem 4WE

Value of $x=11$

Explanation of Solution

Given:

The given figure is,

  

From the given figure,

Side $AB=10,BC=11,\angle BAC={63}^o,\angle ABC={54}^0$ and $AB=x$

From the triangle ABC,

  $\begin{array}{l}\angle ABC+ACB+\angle BAC={180}^o\\ {54}^o+\angle ACB+{63}^o={180}^o\\ \Rightarrow \angle ACB={63}^o\end{array}$

i.e. $\angle ACB=\angle BAC={63}^o$

So, $\Delta ABC$ is isosceles triangle.

So,

  $\begin{array}{l}AB=BC=11\\ \Rightarrow BC=x=11\end{array}$

Therefore, $x=11$