Question

In triangle $ABC$ shown, $AB=1.5\left(AC\right)$ and $BC=10$. The perimeter of the triangle is $25$. If $m\angle ACB={35}^o$, what is the value of $m\angle ABC$?

• A. ${59.4}^o$
• B. ${22.5}^o$
• C. ${35}^o$
• D. ${42.6}^o$
• E. ${24}^o$

Answer 1

The correct option is B ${22.5}^o$

Given, $AB=1.5AC$ , $BC=10$ , perimeter is $AB+BC+CA=25$
So, we get $2.5AC+10=25$ $\Rightarrow AC=6$ and $AB=9$
By sine rule , we get $\frac{AC}{\sin B}=\frac{AB}{\sin C}$
$\Rightarrow \sin B=\frac{6\sin \left(35\right)}{9}=0.3824$
$\Rightarrow B=arc\sin \left(0.3824\right)=22.5$ degrees