Solve the triangle. A = 45°, a = 33 and b = 26

Solution:

Given A = 45°, a = 33 and b = 26

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

solving the triangle using the law of sines

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

Consider first two fractions to find B

Sin45° / 33 = sinB / 26

sinB/26 = 0.7071/33 = 0.021

sinB = 26 × 0.0211 = 0.546

B = sin^-1(0.546)

B = 34.34°

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

A + B + C = 180°

46° + 34.34° + C = 180°

C = 180° - 80.34

C = 99.66°

From sinA/a = sinC/c, we have sin46° /33 = sin(99.65)/c

0.98/c = 0.021

c = 0.98/0.021

c = 45.42

Hence, A = 45°, B = 34.34°, C = 99.66°

a = 33, b = 26, c = 45.42

Summary:

By solving the triangle, we get A = 45°, B = 34.34°, C = 99.66°, a =33, b = 26, c = 45.42