i really need help i dont know how to slove this home work please help

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 = 46,    c = 44,    ∠C = 31°

∠A1 =	1 °		∠A2 =	2 °
∠B1 =	3 °		∠B2 =	4 °
a1 =	5		a2 =	6

 

Answer 1

Step 1:

The sides of the triangle are  and .

The angle of triangle .

Solve the triangle by using Law of Sines.

Apply law of sines formula: .

Consider .

Substitute ,  and  in .

.

The angle  and .

For both the choices of , .

Therefore, two choices satisfies the condition of triangles.

There exists two triangles with these measurements.

Step 2:

The sum of three angles in a triangle is .

Substitute  and .

.

Substitute  and  in .

.

Step 3:

Find other side.

Consider .

Substitute ,  and  in .

Step 4:

Consider .

Substitute ,  and  in .

Solution:

,  and .

,  and .