Question

In $△ABC,\angle B={90}^{\circ },BC=7$ and $AC-AB=1$,

then $\sin C=.....$

• A. $\frac{21}{22}$
• B. $\frac{22}{23}$
• C. $\frac{23}{24}$
• D. $\frac{24}{25}$

Answer 1

The correct option is D $\frac{24}{25}$

$AC-AB=1$

$\therefore AC=AB+1$

In $△ABC$

$A{C}^2=A{B}^2+B{C}^2$ ...(By pythagoras)

$\therefore (AB+1{)}^2=A{B}^2+B{C}^2$

So, $1+2AB+A{B}^2=A{B}^2+B{C}^2$
$\therefore 1+2AB=(BC{)}^2=2AB=(7{)}^2-1=49-1=48$

So, $AB=\frac{48}{2}=24$ and $AC=AB+1=25$

So, $\sin C=\frac{24}{25}$. Hence $\frac{24}{25}$ is correct.