Trigonometry of 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

This is the ambiguous case (2 solutions) because c is less than 49 and greater than 49Sin34 which is 27.4.

So use the Law on Sines to find Angle B as as follows.

SinC/c = SinB/b

Sin34/45 = SinB/49

B = 37.5 deg

This is the result on the calculator but we also know that there is another angle between 90 deg and 180 deg with the same Sine.

That angle is 180 - 37.5 = 142.5 deg

So you will answer that B2 = 37.5 and B1 = 142.5 (Because they want A1 to be the smaller of the Angle A's then B2 will be the smaller of the Angle B's.)

A1 = 180 - 34 - 142.5= 3.5 deg

A2 = 180 - 34 - 37.5 = 108.5 deg

We will again use the Law of Sines to find the values of a.

SinA1/a1 = SinC/c

Sin3.5/a1 = Sin34/45

a1 = 4.9

SinA2/a2 = SinC/c

Sin108.5/a2 = Sin34/45

a2 = 76.3