Solve the triangle. A = 45°, b = 34, c = 27

Solution:

Given A = 45°, a = 34 and b = 27

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

Sin46° / 34 = sinB / 27

sinB/27 = 0.7193/34 = 0.021

sinB = 27 × 0.0211 = 0.5712

B = sin^-1(0.5712)

B = 34.83°

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

A + B + C = 180°

46° + 34.83° + C = 180°

C = 180° - 80.83

C = 99.16°

From sinA/a = sinC/c, we have sin46° /34 = sin(99.16)/c

0.98/c = 0.0211

c = 0.98/0.021

c = 46.78

Hence, A = 46°, B =34.83° , C = 99.16°

a = 34, b = 27, c = 46.78

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Solve the triangle. A = 45°, b = 34, c = 27

Summary:

By solving the triangle, we get A = 46°, B =34.83° , C = 99.16°, a = 34, b = 27, c = 46.78