C Secure I https://www.m MATH 1316.006 Homework: 8.3 HW Score: 0 of 1 pt 8.3.41

Question

C Secure I https://www.m MATH 1316.006 Homework: 8.3 HW Score: 0 of 1 pt 8.3.41 Solve the following triangle using either the Law of Sines or the Law of Cosines. b-5, c 12, A-58" Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice Do not round until the final answer. Then round to one decimal place as needed) There is only one possible solution forthe triangle The measurements for the remaining side a and angles B and C are as follows ans 0 A. 0 ns for the triangle The measurements for the solution with the smaller angle B are as follows The measurements for the solution with the larger angle B are as follows ° C. There are no possible solutions for this triangle All parts showing

Explanation / Answer

Solution:

Given: b = 5, c = 12, and Angle A = 58°

using the Law of Cosines;

a2 = b2 + c2 - 2bccos(A)
a2 = 52 + 122 - 2(5)(12)cos(58°)
a2 = 25 + 144 - 63.59
a2 = 105.41
a ? 10.27

sin(A)/a = sin(B)/b
sin(58°)/a = sin(B)/5
5sin(58°)/10.27 = sin(B)
sin(B) ? 0.41287
B ? 24.38°
C = 180 - A - B = 180 - 58 - 24.38
C ? 97.62°

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