HELP WITH MY TRIG HW: Side-Angle-Side Triangles *Best Answer Awarded*?

Whatever the triangle, you can apply the Law of sines.

a/sin(A) = b/sin(B) = c/sin(C) → you can adapt it to your case

a/sin(A) = 40/sin(32) = 45/sin(C)

40/sin(32) = 45/sin(C)

40.sin(C) = 45.sin(32)

8.sin(C) = 9.sin(32)

sin(C) = (9/8).sin(32)

→ C ≈ 36.5953 °

Whatever the triangle, the sum of the 3 angles is always 180 °.

A + B + C = 180

A = 180 - B - C → given that: B = 32 °

A = 148 - C → recall: C ≈ 36.5953 °

→ A ≈ 111.4047 °

a/sin(A) = c/sin(C)

a = c.sin(A)/sin(C) → given that: c = 45

a = 45.sin(A)/sin(C) → we’ve just seen that: C ≈ 36.5953 ° and we’ve just seen that: A ≈ 111.4047 °

→ a ≈ 70.27681

By the cosine rule,

40^2=a^2+45^2-2(45)acos(32*)

=>

a^2-76.3243a+425=0

=>

a=6.0475 or a=70.2768

approximately.

(1) a=6.0475. By the sine rule,

6.0475/sinA=40/sin(32*)

=>

A=4.5953* approximately

C=180*-32*-4.5953*=143.4047*

(2)a=70.2768.

C=36.5953*

A=180*-32*-36.5953*=111.4047*

Ans. there is are 2 solutions:

(1) a=6.1, A=4.6*, C=143.4*;

(2) a=70.3, A=111.4*, C=36.6*

approximately.

Memorize the key word: SohCahToa

Sin = Opposite side / Hypotenuse

Cos = Adjacent side / Hypotenuse

Tan = Opposite side / Adjacent side

You are given the lengths of the sides, use the relations above to find the tangent of the angle, plug the number into your calculator and hit the arctan key.

These relations are at the root of trigonometry, without knowing them you can't proceed any further.