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Solve the triangle using the Law of Sines. (Assume b and c = 20, and ∠C = 63°. Round the length to two decimal places.)

Solve the triangle using the Law of Sines. (Assume b and c = 20, and ∠C = 63°. Round-example-1
User Zhenhir
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Answer:

a = 16.51

angle A = 54

angle B = 63

Explanation:

Recall the law of sines:

sinA/a = sinB/b = sinC/c

We know c is 20, and angle C is 63. Since b is also 20, angle B must also be 20. We know have two of the 3 angles, summing to 126, and we can find the last angle from that. 180-126=54, so angle A must be 54.

To solve for a, we need to know the ratio of the other two terms. Sin(63) is around 0.99, and 0.99/20 is 0.049. So we have 0.049=sin(54)/a. To solve for a, we divide by sin(54) and take the reciprocal of both sides, giving a = (sin54)/0.049, which is about 16.51, which is the length of the side a.

User Aslak Knutsen
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