Trigonometry (beginner) help?

Question

I need help setting these up. I can work them out, but I can't figure out the formulas.

a) lowercase letters are the sides and uppercase are the angles a=42, c=60, (measure of angle)B=58 Find: b, A, and C

b) (measure of angle)A=43, b=23, c=26 Find: a, b, and c a=16,

c) a=16, (measure of angle)A=23, (measure of angle)B=87
Find: b, c, and C (which I found was 70)

d) c=15, a=12.9, b=18.4
Find: A, B, C

Answer 1

Step 1:

The sides of the triangle are and the angle .

Law of cosines: .

Substitute and in above cosine rule.

side .

Step 2:

Law of sines: .

Substitute and in above formula.

In a triangle, total of three angles is .

Substitute  and in above expression.

side and angles and .

Solution:

side and angles and .

Answer 2

Step 1:

(b) The sides of the triangle and angle .

Law of cosines: .

substitute and in above formula.

Side

Step 2:

(c) The two angles of the triangle is and side

In a triangle, total of three angles is .

Substitute  in above expression.

Thus, the third angle .

Law of sines: .

Substitute and in  above formula.

Law of sines: .

Substitute and in above formula.

solution:

(b) Side .

(c) , and .

Answer 3

Step 1:

(d) The sides of the triangle are and .

Law of cosines: .

Substitute and in above formula.

Step 2:

Law of sines: .

Substitute and in above formula.

In a triangle, sum of the three angles is .

Substitute  and in above expression.

The three angles of the triangle are , and .

Solution:

The three angles of the triangle are , and .