The given question is incomplete, the real question is;
In triangle ABC .m∠A=35° ,m∠B=65° , and a=8.71. Use the law of sines to find b. Round your answer to the nearest tenth.
Options:
(A) 13.8
(B) 9.5
(C) 8.7
(D)23.7
Answer:
The length of the unknown side 'b' is 13.8.
What is the law of sines?
The law of sines states that the ratio of the side length of a triangle to the sine of the opposite angle is the same for all three sides.
(a/sin A) = (b/sin B) = (c/sin C)
In the triangle ABC,
∠A = 35°
∠B = 65°
The side opposite to the ∠A is 'a' and the side opposite to ∠B
The length of side 'a' is a = 8.71
Therefore, substitute the values in the law of sines equation to find the length of unknown side 'b'
b = (a/sin A) × sin B
b = (8.71/sin 35°) × sin 65°
b = (8.71/sin 35°) × sin 65°
b = (8.71/0.573)×0.906
b = 15.2×0.906
b = 13.77
Round the length to the nearest tenth that is, b ≈ 13.8
Hence option (A) is correct.
Learn more about the law of sines at https://brainly.com/question/4372174
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