Solve the triangle. A = 33°, a = 19, b = 14

Solution:

Given A = 33°, a = 19, b = 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 = sinB / 14

sinB/14 = 0.544/19 = 0.02

sinB = 0.02(14) = 0.40

B= sin^-1(0.40)

B= 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°

C = 180° - 56.57

C = 123.43°

From sinA/a = sinC/c,we have sin33°/19 = sin123.43°/c,

0.83/c = 0.544/19 = 0.028

c = 0.83/0.028

c = 29.64

Hence, A = 33°, B = 23.57°, C = 123.43°

a = 19, b = 14, c = 29.64

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Solve the triangle. A = 33°, a = 19, b = 14

Summary:

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