Solvethe triangle with a 419 c 553 and beta 273 degree b

Solvethe triangle with a = 4.19, c = 5.53, and beta = 27.3 degree. b allmostequalto (Type an integer or a decimal rounded to one decimal place as needed) alpha allmostequalto degree (Type an integer or a decimal rounded to one decimal place as needed) gamma degree Type an integer or a decimal rounded to one decimal place as needed

Solution

a = 4.19

c = 5.53

beta = 27.3 degrees

applying law of cosines to solve the triangle

b^2 = a^2 + c^2 - 2ac cos 27.3

b^2 = 5.53^2 + 4.19^2 - 2(5.53)(4.19) cos 27.3

b^2 = 48.137 - 41.180

b = 2.638

applying law of sines

b / sin beta = a / sin alpha

2.638 / sin 27.3 = 4.19 / sin alpha

5.7516 = 4.19/ sin alpha

alpha = 78.6867 degrees

5.7516 = 5.53 / sin gama

gama = sin^-1 ( 5.53 / 5.7516) = 74.04 degrees