Question

What is the measure of ∠K, to the nearest degree?

13
24
66
72

Answer 1

66is my first choice answer

Answer 2

In the given triangle, we have to find the measure of $\angle K$ to the nearest degree.

By applying law of sine which states

"In a triangle ABC, with angles A, B and C and side opposite angle A is 'a', side opposite to angle B is 'b' and side opposite to angle C is 'c'. Therefore, the sine law is:

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Now, applying law of sine in the triangle JLK, $\angle L=76^{\circ} , l=53, k=50$

Therefore, $\frac{\sin J}{j}=\frac{\sin K}{k}=\frac{\sin L}{l}$

Using the ratio, $\frac{\sin K}{k}=\frac{\sin L}{l}$

$\frac{\sin K}{50}=\frac{\sin 76}{53}$

$\sin K=\frac{\sin 76 \times 50^{\circ}}{53}$

$\sin K=0.915$

$\angle K=\arcsin 0.915$

$\angle K= 66.2$

Therefore, $\angle K= 66^{\circ}$

Therefore, Option 3 is the correct answer.