SOLUTION: Solve triangle ABC where A = 25 degrees, a = 9cm, and c = 11cm. Include the ambiguous case

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Question 1085658: Solve triangle ABC where A = 25 degrees, a = 9cm, and c = 11cm. Include the ambiguous case
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve triangle ABC where A = 25 degrees, a = 9cm, and c = 11cm.
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Use the Law of Sines to find angle C.
sin(A)/a = sin(C)/c
Angle B = 180 - (A + C)
Then find side b.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given: A+=+25 degrees, a+=+9cm, and c+=+11cm
The ambiguous case of the sine law, where two sides and one angle are given.

a+%2F+sin%28A%29+=+c+%2F+sin%28C%29+ if A+=+25 degrees,+a+=+9cm, and c+=+11cm, we have

9cm+%2F+sin%2825%29+=+11cm+%2F+sin%28C%29+

9cm%2Asin%28C%29+=+11cm+%2Asin%2825%29+

sin%28C%29++=+%2811cm%2F9cm%29+%2Asin%2825%29+

sin%28C%29+=+1.222222222222222+%2A0.42261826+

C+=sin%5E-1%280.51653342888888879497372%29+

C+=31.100006692833242512632°

C+=31.1°

B=180-%2825%2B31.1%29=180-56.1=123.9

a+%2F+sin%28A%29+=+b+%2F+sin%28B%29+

b=%28a+%2Asin%28B%29+%29%2F+sin%28A%29++

b=%289cm+%2Asin%28123.9%29+%29%2F+sin%2825%29++

b=%289cm+%2A0.830012+%29%2F+0.42261826++

b=7.470108cm+%2F+0.42261826++

b=17.7cm