Solve the triangle. B = 33°, b = 19, c = 14

Solution:

Given Given B = 33°, b = 19, c = 14

According to the law of sines, we have sinA/a = sinB/b = sinC/c

Where A,B,C are angles and a,b,c are sides

Consider first two fractions to find B

Sin33° / 19 = sinC / 14

sin C/14 = 0.544/19 = 0.02

sin C = 0.02(14) = 0.40

C = sin^-1(0.40)

C= 23.57°

We know that the sum of all angles in a triangle is equal to 180°.

A + B + C = 180°

33° + 23.57° + C = 180°

A = 180° - 56.57

A = 123.43°

From sinA/a = sinB/b,we have sin33°/19 = sin123.43°/a,

0.83/a = 0.544/19 = 0.028

a = 0.83/0.028

a = 29.64

Hence, A =123.43°, B = 33°, C =23.57°

a = 29.64, b = 19, c = 14

Summary:

By solving the triangle, A =123.43°, B = 33°, C =23.57° and a = 29.64, b = 19, c = 14