Consider a triangle ABC like the one below. Suppose that a = 47, b = 59, and A = 37" (The figure is not drawn to scale.) Solve the triangle, Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If no such triangle exists, enter "No solution." If there is more than one solution, use the button labeled "or",

B = 49.1°

C = 93.9°

c = 77.9

Step-by-step explanation:

Given:

a = 47, b = 59, and A = 37°

Required:

B, C, and c

Solution:

✔️To find B, apply the law of sines:

Plug in the values

Cross multiply

Divide both sides by 47

B = 49.0690779° ≈ 49.1° (nearest tenth)

✔️C = 180° - (A + B) (sum of triangle)

C = 180° - (37° + 49.1°)

C = 93.9°

✔️To find c, apply the law of sines:

Plug in the values

Cross multiply

Divide both sides by sin(49.1)

c = 77.8766982

c ≈ 77.9 (nearest tenth)

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: