Question

From the informating given in the figure, find the value of x and also sides AC and BC.

Answer 1

Sum of all $\angle s$ of a $△={180}^o$

$\therefore 3x+2x+x={180}^o$ [Ref. image 1]

$\Rightarrow 6x={180}^o$

$\Rightarrow x={30}^o$

In $△ABC,$

$\angle ={90}^o,\angle B={60}^o,\angle C={30}^o$ [Ref. image 2]

$\tan {60}^o=\frac{AC}{AB}$

$\sqrt{3}=\frac{AC}{5}$

$\therefore AC=5\sqrt{3}cm$

$\cos {60}^o=\frac{AB}{BC}$

$\frac{1}{2}=\frac{5}{BC}$

$\therefore BC=10cm$