i really need help i dont get it

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 = 45,    c = 43,    ∠C = 38°

∠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 .