SOLUTION: In a triangle ABC the angle A is 62 degrees, and the lengths of two sides are, a=6 and side b=10. What is the length of side c. One of the following possible answers follow A)

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Question 1198059: In a triangle ABC the angle A is 62 degrees, and the lengths of two sides are, a=6 and side b=10. What is the length of side c.
One of the following possible answers follow
A) 6
B) 8
C) 10
D) 12
E) None of these
Found 3 solutions by Edwin McCravy, MathLover1, ikleyn:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


The above drawing is approximately to scale. And as you see the
side a = CB = 6 is too short to reach down to make a triangle of
any kind, because angle A=62o opens too wide.  So I predict there 
is no solution.

This is the ambiguous case, ASS, which can have 0,1, or 2 solutions.
Let's show it has 0 solutions with the law of sines:

a%2Fsin%28A%29=b%2Fsin%28B%29=c%2Fsin%28C%29

6%2Fsin%2862%5Eo%29=10%2Fsin%28B%29

6sin%28B%29=10sin%2862%5Eo%29

sin%28B%29=%2810sin%2862%5Eo%29%29%2F6

sin%28B%29=%2810%280.8829475929%29%29%2F6

sin%28B%29=1.471579321

No sine can ever be more than 1.  So there is no solution.

Edwin

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

given:
A=+62 degrees
+a=6
+b=10

use The Law of Cosines
a%5E2+=+b%5E2+%2B+c%5E2+-+2bc+%2A+cos%28A%29
6%5E2+=+10%5E2+%2B+c%5E2+-+20c+%2A+cos%2862%29.................cos%2862%29+≈0.469472
36=+100%2B+c%5E2+-+20c+%2A0.469472
c%5E2-+9.38944c%2B100-36=0
c%5E2-+9.38944c%2B64=0..........using quadratic formula we get
c+=+4.69472+-+6.47762%2Ai
c+=+4.69472+%2B+6.47762%2Ai

since solutions are complex umbers, a triangle with such parameters doesn't exist
answer:
E) None of these

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

I solved this problem and answered this question at this forum several days ago,
saying that such triangle as described in the post does not exist.


See the link

https://www.algebra.com/algebra/homework/Angles/Angles.faq.question.1197886.html

https://www.algebra.com/algebra/homework/Angles/Angles.faq.question.1197886.html