Solve the triangle. A = 46°, a = 33, 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

using the sine law to solve the triangle

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

Consider first two fractions to find B

Sin46°/33 = sinB/26

sinB/26 = 0.7193/33 = 0.021

sinB = 27 × 0.0211 = 0.56

B = sin^-1(0.56)

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° - 80.83

C = 99.65°

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 = 46°, B = 34.34° , C = 99.65°

a = 33, b = 26, c = 45.42

Summary:

By solving the triangle, we get A = 46°, B = 34.34°, C = 99.65°, a = 33, b = 26, c = 45.42

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