Question

What is the approximate measure of angle K? Use the law of sines to find the answer.

Answer 1

Answer:

B. 34°

Step-by-step explanation:

We have been given an image of a triangle and we are asked to find the measure of angle K.

We will use law of sines to solve our given problem.

$\frac{Sin(A)}{a}=\frac{Sin(B)}{b}=\frac{Sin(C)}{c}$, where, a, b and c are sides corresponding to angle A, angle B and angle C respectively.

Upon substituting our given values in above formula we will get,

$\frac{Sin(K)}{2.7}=\frac{Sin(105^{\circ})}{4.7}$

Upon multiplying both sides of our equation by 2.7 we will get,

$\frac{Sin(K)}{2.7}\times 2.7=\frac{Sin(105^{\circ})}{4.7}\times 2.7$

$Sin(K)=\frac{0.965925826289}{4.7}\times 2.7$

$Sin(K)=0.2055161332529787\times 2.7$

$Sin(K)=0.55489355978304249$

Now we will use arcsin to find the measure of angle K.

$K=Sin^{-1}(0.55489355978304249)$

$K=33.703383757351^{\circ}$

Upon rounding our answer to nearest whole number we will get,

$K\approx 34^{\circ}$

Therefore, the measure of angle K is approximately 34 degrees and option B is the correct choice.

Answer 2

34 should be the answer