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)

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)   (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=62^o 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: No sine can ever be more than 1. So there is no solution. Edwin

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

given:
degrees

use The Law of Cosines

.................≈

..........using quadratic formula we get

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

Answer by ikleyn(52803)   (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

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