Question

In $\Delta ABC$, if $\angle C=3\angle A,BC=27$ and $AB=48$. Then the value of $AC$ is

• A. $5$
• B. $35$
• C. $7$
• D. $6$

Answer 1

The correct option is B $35$

Given $\angle C=3\angle A,BC=27$ and $AB=48$
Using the sine law, we get
$\frac{27}{\sin A}=\frac{48}{\sin 3A}\Rightarrow 3-4{\sin }^{2}A=\frac{16}{9}$
${\sin }^{2}A=\frac{11}{36}$
Now $\frac{b}{27}=\frac{\sin 4A}{\sin A}$
$\Rightarrow \frac{b}{27}=\frac{2\sin 2A\cos 2A}{\sin A}=\frac{4\sin A\cos A\cos 2A}{\sin A}$
$\Rightarrow \frac{b}{27}=4\sqrt{1-{\sin }^{2}A}(1-2{\sin }^{2}A)$
$\Rightarrow b=AC=35$