Trigonometry Angles

Question

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠A₁ is smaller than ∠A₂.)

b = 49,    c = 45,    ∠C = 34°

Find Angle A1=

Angle A2 =

Angle B1 =

Angle B2 =

a1 =

a2 =

Answer 1

You are given b, c, and angle C which I assume is opposite side c.

You can find B from law of sines sinB/b = sinC/c or B = sin^-1(bsinC/c) = sin^-1(49sin(34°)/45) = 37.51 or 142.49.

You can now find side A_i = 180 -B_i -C

a is obtained from cos law

a_i² = b²+c²-(2bc)cos(A_i)

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