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storchak [24]
3 years ago
11

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

Mathematics
2 answers:
Pavlova-9 [17]3 years ago
8 0

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.

VMariaS [17]3 years ago
5 0
34 should be the answer

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