Let ΔABC be a triangle such that b=√8, c=√30, and cos(B)=5/√30. Find all possible values for side length a, entering your answer as a comma-separated list in increasing order.

Answer 1

you have cosB. Use that to get cosA.

Now you cab find angle A using the law of sines:

sinA/a = sinB/b

Now, use the law of cosines to get side a:

a^2 = b^2+c^2 - 2bc cosA

Answer 2

sorry: 1st step is use cosB to get sinB.