Question

For triangle ABC with c=345, a=534, and C=25.4 degree, there are two possible values for angle A. What are they?

Answer 1

We can use the law of sines there

\[\large \frac{sin(25.4)}{345} = \frac{A}{534}\]

And solve for A

Answer 2

i got it but it has 2 different values man

Answer 3

one i got is 44.43 degree

Answer 4

any clue guys?

Answer 5

How did you even get 44.3? I got 41.6 degrees.

Answer 6

The other answer could therefore be (180-41.6)= 138.4 degrees.

Answer 7

lol...my bad...the correct answer is 41.6

Answer 8

Hmm...I'm not entirely sure on that

It states that angle A can have 2 answers...since angle A will always oppose side 'a' it will always be in the same ratio plugged into the law of sines...it can never be what angle B will be which would be the 138.4 degrees

Frankly I'm not sure how 1 angle can have 2 different values if side lengths are given as they are

Answer 9

this is the point that confused me, but this is the question i got in book...so....

Answer 10

Guess I should post something here.
When you are given two sides and a NON-INCLUDED angle, two triangles can sometimes result. (see graphic).
Notice that the 3 items of given information - (25.4° angle and sides of 534 and 345) remain the same in both triangles. However, angles A and B and side b do change.

Just thought I'd show how you can get two triangles when given 2 sides and a non-included angle,

More information and a calculator are located here:
http://www.1728.org/trigssa.htm