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.
[tex]\frac{Sin(A)}{a}=\frac{Sin(B)}{b}=\frac{Sin(C)}{c}[/tex], 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,
[tex]\frac{Sin(K)}{2.7}=\frac{Sin(105^{\circ})}{4.7}[/tex]
Upon multiplying both sides of our equation by 2.7 we will get,
[tex]\frac{Sin(K)}{2.7}\times 2.7=\frac{Sin(105^{\circ})}{4.7}\times 2.7[/tex]
[tex]Sin(K)=\frac{0.965925826289}{4.7}\times 2.7[/tex]
[tex]Sin(K)=0.2055161332529787\times 2.7[/tex]
[tex]Sin(K)=0.55489355978304249[/tex]
Now we will use arcsin to find the measure of angle K.
[tex]K=Sin^{-1}(0.55489355978304249)[/tex]
[tex]K=33.703383757351^{\circ}[/tex]
Upon rounding our answer to nearest whole number we will get,
[tex]K\approx 34^{\circ}[/tex]
Therefore, the measure of angle K is approximately 34 degrees and option B is the correct choice.
