The measures of two sides of a triangle and the angle opposite one of them are given. Solve all possible triangles if any. Please show your solutions.

Question

b = 5649, a = 6382, β = 59.43°

Answer 1

Use sin laws: sinα/a = sinβ/b = sinγ/c

Solve for angle α given a,b,β α = sin^-1((a/b)sinβ) plug in. There will be two answers because 180-α is also a solution not included. (The inverse sine is limited to a range from -90 to 90)

Solve for c given that γ = 180 - α - β: c = b sinγ/sinβ for both cases (or you can use cos law)

Make sure to check that the sin law expressions are correct when you are done