Use the Law of Sines to solve for all possible triangles that satisfy the given conditions.

Question

There may be two triangles, one triangle, or no triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Enter all angles in degrees. Round your answers to one decimal place. Below, enter your answers so that ∠A₁ is smaller than ∠A₂.)

b = 49,   c = 46,   ∠C = 32°

∠A₁

    ∠A₂

 °∠B₁

°∠B₂

°a₁

a₂

Answer 1

sin32°/46 = sinB / 49

sinB = 49sin32° / 46 = 0.5546792

∠B = Sin^-1(0.5546702) or 180º - Sin^-1(0.5546792) = 34.4° or 145.6°

First triangle: ∠C = 32°, ∠B = 34.4°, ∠A = 113.6°, b = 49, c = 46, use Law of Sines to find a

Second triangle: ∠C = 32°, ∠B = 145.6°, ∠A = 2.4°, b = 49, c = 46, use Law of Sines to find a

Answer 2

If 46 = hypotenuse, one triangle

If 46 < hypotenuse, one triangle

If 46 > hypotenuse, two triangles.

Draw and label a diagram and answer.