Solve the SSA triangle. Indicate whether the given measurements result in no tri

Question

Solve the SSA triangle. Indicate whether the given measurements result in no triangle, one triangle, or two triangles. Solve each resulting triangle. Round each answer to the nearest tenth. B = 44degree b = 30 c = 41 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. There are two possible solutions for the triangle. The measurements for the solution with the longer side a are as follows. A_1 = degree C_1 = degree a_1 = The measurements for the solution with the shorter side a are as follows. A_2 = degree C_2 = degree a_2 = (Round to the nearest tenth as needed.) There is only one possible solution for the triangle. The measurements for the remaining angles A and C and side a are as follows. A = degree C = degree A = (Round to the nearest tenth as needed.) There are no possible solutions for the triangle.

Explanation / Answer

B = 44deg ; b = 30 ; c= 41

use sine rule:

b/sinB = c/sinC

30/sin44 = 41/sinC

sinC = 41*sin44/30 = 0.949

C1 = 71.69 = 71.7 deg

C2 = 180 - 71.69 = 108.31 = 108.3 deg

A1 = 180 - B - C1 = 64.31 = 64.3 deg

A2 = 180 - B - C2 = 27.69 = 27.7 deg

a1/sinA1 = b/sinB

a1 = sin64.31*30/sin44 = 38.92 = 38.9

a2/sinA2 = b/sinB

a2 = sin27.69*30/sin44 = 20.06 = 20.1

Option A

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