Question

Find the value of $\sin \angle M$ in the right angled triangle shown in the above figure.

• A. $\frac{10}{12}$
• B. $\frac{12}{10}$
• C. $\frac{\sqrt{44}}{10}$
• D. $\frac{10}{\sqrt{44}}$
• E. $\frac{\sqrt{44}}{12}$

Answer 1

Answer: (E)

$\frac{\sqrt{44}}{12}$

In a right-angled triangle with angle $L=$ ${90}^{\circ }$

Using Pythagorean theorem

$(MK{)}^2=(ML{)}^2+(KL{)}^2$

$(KL{)}^2=(MK{)}^2-(ML{)}^2$

$KL=\sqrt{(MK{)}^2-(ML{)}^2}$

Put the value from the figure, we get

$KL=\sqrt{{12}^2-{10}^2}$

$KL=\sqrt{144-100}$

$KL=\sqrt{44}$

$\sin M=$ $\frac{Perpendicular}{Hypotenuse}=\frac{KL}{MK}=\frac{\sqrt{44}}{12}$