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
Accepted Solution
A:
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