Question

In the given figure, $BC=15cm$ and $\sin B=\frac{4}{5}$, What is the value of $AB$?

• A. $25cm$
• B. $20cm$
• C. $5cm$
• D. $4cm$

Answer 1

The correct option is A $25cm$

$\sin B=\frac{AC}{AB}=\frac{\sqrt{A{B}^2-B{C}^2}}{AB}$

$\frac{4}{5}AB=\sqrt{A{B}^2-{15}^2}$

$\Rightarrow 16A{B}^2=25A{B}^2-\left(25\right)(15{)}^2$

$A{B}^2=\frac{25\times 15\times 15}{9}$

$\Rightarrow AB=25$