Solve the triangle. a = 10, b = 23, C = 95°

Solution:

Given a = 10, b = 23, C = 95°

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

c² = 10² + 23² - 2(10)(23) cos(95)

c² = 100 + 529 - 460(-0.087)

c² = 629 + 40.06

c² = 669.06

c= √(669.06) = 25.86

We have the law of sines as follows:

sinA/a = sinC/c

sinA/10 = sin95/ 25.86

sinA = 0.385

A = sin^-1(0.385)

A = 22.64°

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

A + B + C = 180°

22.643° + B + 95° = 180°

B = 180°- 117.64°

B = 62.35°

Hence, A = 22.64°, B = 62.35°, C = 95°

a = 10,b = 23, c = 25.86

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Solve the triangle. a = 10, b = 23, C = 95°

Summary:

By solving triangle, we get A = 22.64°, B = 62.35°, C = 95°, a = 10,b = 23, c = 25.86