Given that A=43 degrees, B=82 degrees and c=28, solve triangle ABC. Round to the nearest hundredth. A) C = 93 degrees, b = 33.8, a = 23.3 B) C = 55 degrees, b = 33.8, a = 23.3 C) C = 55 degrees, b = 23.3, a = 33.8 D) C = 93 degrees, b = 23.3, a = 33.8

A=43°

B=82°

c=28

1) A+B+C=180°

Replacing A=43° and B=82° in the equation above:

43°+82°+C=180°

125°+C=180°

Solving for C. Subtracting 125° both sides of the equation:

125°+C-125°=180°-125°

C=55° (option B or C)

2) Law of sines

a/sin A=b/sin B=c/sin C

Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:

a/sin 43°=b/sin 82°=28/sin 55°

2.1) a/sin 43°=28/sin 55°

Solving for a. Multiplying both sides of the equation by sin 43°:

sin 43° (a/sin 43°) = sin 43° (28/sin 55°)

a=28 sin 43° / sin 55°

Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044

a=28 (0.681998360) / 0.819152044

a=23.31185549

Rounded to one decimal place

a=23.3

2.2) b/sin 82°=28/sin 55°

Solving for a. Multiplying both sides of the equation by sin 82°:

sin 82° (b/sin 82°) = sin 82° (28/sin 55°)

b=28 sin 82° / sin 55°

Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044

b=28 (0.990268069) / 0.819152044

b=33.84903466

Rounded to one decimal place

b=33.8

Answer: Option B) C=55°, b=33.8, a=23.3