The measures of two sides of a triangle and the angle opposite one of them are given. Determine the number of triangles that satisfy the given set of conditions. (With solution and explanation pls)

Question

a) b = 27, a = 46, β = 38°

b) a = 245, b = 302, α = 136.4°

Answer 1

Answer 2

Use the Law of sines and arcsin to determine the measure of angle A

A = arcsin( a*sin(B)/b ).

Use the Triangle Angle Identity to find angle C

C = 180 - A - B

Use the law of cosines to find the length of side c

c = sqrt( a² + b² - 2ab cos(C) )

Solve these values and you have completed the triangle.