. (5 points) For each of the given triangles ABC, determine if there is one, mul
ID: 3149339 • Letter: #
Question
. (5 points) For each of the given triangles ABC, determine if there is one, multiple, or no ways to solve the triangle. If there is one way to solve the triangle, find the remaining sides and angles. If there is more than one way to solve the triangle, solve one of the possible triangles, and explain how you would solve the other triangle (that is, what would be different). Round answers to the nearest 0.1, and explain your reasoning/show your work where appropriate (a) ZA-41.6°, a 168.4, and b 246.8 112.9, and b- 209.3 (b) LA 43.7°, aExplanation / Answer
(a)
by law of sines a/sinA=b/sinB=c/sinC
=>168.4/sin41.6o=246.8/sinB.
=>sinB=(246.8/168.4)sin41.6o
=>B=76.7o,B=103.3o
A+B+C=180o
=>41.6o+76.7o+C=180o,41.6o+103.3o+C=180o
=>C=61.7o ,C=35.1o
168.4/sin41.6o=c/sin61.7o,168.4/sin41.6o=c/sin35.1o
=>c =168.4sin61.7o/sin41.6o ,c=168.4sin35.1o/sin41.6o
=>c =223.4 ,c=145.7
two sets of solution are
B=76.7o,C=61.7o,c =223.4
B=103.3o ,C=35.1o ,c=145.7
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(b)
by law of sines a/sinA=b/sinB=c/sinC
=>112.9/sin43.7o=209.3/sinB.
=>sinB=(209.3/112.9)sin43.7o
=>sinB=1.2807944077802166197760714035919
no solution
so no triangle exists
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