Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is larger than ∠B2.) a = 36, c = 48, ∠A = 39°

Find angles; B1, B2, C1, C2

Find sides; b1, b2

57.0°, 123.0°

84.0°, 96.0°

56.9,

Step-by-step explanation:

Given:

a = 36, c = 48, ∠A = 39°

∠B1 is larger than ∠B2

Find attached the diagram.

We would apply sine rule to find ∠C

a/sinA = c/sinC

36/sin39° = 48/sinC

36sinC = 48sin39

sinC = 48sin39/36 = 48(0.6293)/36

sin C = 0.8391

C = arcsin(0.8391)

C= 57.045

∠C1 = C = 57.0° (1 decimal place)

For sine rule, angles which give same value are x and (180-x)

If C= x = 57.0°

180-x = 180 - 57.0° = 123°

∠C2 = 123.0°

sin57° = sin123° = 0.8387

∠A + ∠B + ∠C = 180° (sum of angles I'm a triangle)

39.0 + ∠B +57.0 = 180°

∠B = 180-(39+57)

∠B = 84.0°

∠B1 = 84.0°

∠B2 = 180-∠B1 = 180°-84.0°

∠B2 = 96.0°

∠B1 is smaller than ∠B2

b/sinB = c/sinC

b1/sinB1 = c1/sinC1

b/sin84 = 48/sin57

b = 48sin84/sin57

b = 56.9