Solve the triangle. B = 36°, a = 41, c = 17

Solution:

Given B = 36°, a = 41 and c = 17

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

b² = 41² + 17² - 2(41)(17) cos(36)

b² = 1681 + 289 - 1394(0.8)

b² = 1970 - 1127.74

b² = 842.25

b = √(842.25) = 29

We have the law of sines as follows:

sinA/a = sinB/b

sinA/41 = sin36/ 29

sinA = 41 × 0.02

A = sin^-1(0.82)

A = 55.91°

We know that the sum of all angles of a triangle is 180°

A + B + C = 180°

55.91° + 36°+ C = 180°

C = 180°- 91.91°

C = 88.08°

Hence, A = 55.91°, B = 36°, C = 88.08°

a = 41,b = 29, c = 17

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Solve the triangle. B = 36°, a = 41, c = 17

Summary:

By solving triangle, we get, A = 55.91°, B = 36°, C = 88.08°, a = 41, b = 29, c = 17.