Question

In the given fig., $△JKL$ is equilateral, and $△JKM$ is isosceles. If $\overline{KL}=2$, calculate the distance from $L$ to $M$.

• A. 0.572
• B. 0.636
• C. 0.667
• D. 0.732
• E. 0.767

Answer 1

Answer: (D)

0.732

$KL=2$ which implies $JM=MK=\sqrt{2}$ and $KJ=JL=2$
$\angle$ $MKL=15$ degrees and $\angle$ $KLM=30$ degrees.
By sine rule, we get
$\frac{LM}{\sin 15}=\frac{KM}{\sin 30}=\frac{\sqrt{2}}{\frac{1}{2}}=2\times \sqrt{2}$
$\Rightarrow LM=2\times \sqrt{2}\times \sin 15=0.732$