Solve the triangle. B = 36°, a = 42, c = 18

Solution:

Given B = 36°, a = 41, c = 20

According to the law of cosines, b² = a² + c² - 2ac cos B

b² = 41² + 20² - 2(41)(20)cos(36°)

b² = 1681 + 400 - 1640(0.8090)

b² = 754.24

b =√(754.24)

b = 27.46

According to the laws of sines

SinA/a = SinB/b

sinA/ 41 = Sin36°/ 27.46

sinA = 41 × 0.021

sin A = 0.873

A = Sin^-1(0.873)

A = 60.84°

we know that the sum of all angles of a triangle is 180 degrees.

A + B + C = 180°

60.84 + 36 + C = 180°

C = 180 - 96.8

C = 83.15°

Therefore, B = 36°, a = 42, c = 18, b = 27.46, A = 60.84° and C = 83.15°.

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Solve the triangle. B = 36°, a = 42, c = 18

Summary:

By solving the triangle, B = 36°, a = 42, c = 18 we get b = 27.46, A = 60.84° and C = 83.15°.