14 of 16 10 complete w Solve the triangle if possible C 58 2

14 of 16 (10 complete) w Solve the triangle, if possible. C 58 20\', c 33.4, b 24.5 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. GRound side lengths to the nearest hundredth and angle measures to the nearest minute as needed.) O A. There is one possible solution for the triangle. A side are as follows. The measurements for the remaining angles B and and a A RS O B. There two possible solutions for the triangle. angle B are as follows. The measurements for the solution with the smaller The measurements for the solution with the larger angle B are as follows. O C. There are no possible solutions for this triangle. Click to select and enter your answer(s)

Solution

C = 58deg20\'min = 58.33 deg ; c = 33.4 ; b = 24.5

sin law : b/sinB = c/sinC

sinB = (24.5*sin58.33)/33.4 = 0.624

B1 = 38.63 deg = 38deg38 min ; B2 = 141.37 = 141 deg 22 min

A1 = 180 - 38.63-58.33 = 83.04 deg = 83 deg 2 min

A2 = 180 - 141.37 -58.33 = -ve angle .Not possible

So, only 1 triangle is possible with C =,58deg20\'min ; B1 = 38deg38 min, A1= 83 deg 2 min

a/sinA = b/sinB

a = sin83.04*24.5/sin38.63 = 38.96