The Law of Sines?

The Law of Sines


Determine the number of possible solutions. If a solution exists, solve the triangle. Round angle measures to then nearest minute and side measures to the nearest tenth.


a/SinA = b/SinB = c/SinC








1. A = 38°, B = 63°, c = 15


2. A = 50, a = 33, A = 132°


3. b = 15.2, A = 12°30', C = 57°30'





(I'm not too sure if my teacher wants the time included, i.e. the seconds).








I have a quiz tomorrow, and I have no idea what I'm doing. Can anyone explain? And not tell me to look through some random math site? ;_;

The Law of Sines?
When finding an angle with sine law you might get 0, 1 or 2 answers. When finding a side, only one answer is possible. So on 1 and 3, one solution. You need to add the two given angles then subtract from 180 to get the third. So on 1, C = 180 - (38 + 63) = 180 - 101 = 79





so c/sinC = b/sinB; 15/ sin 101 = b/ sin 63


Cross multiply: b sin 101 = 15 sin 63


Divide both sides by sin 101 and you get b. Find a in the same way.





For 2, something is wrong because you have two different A's. I will guess you meant b = 50





33/sin 132 = 50/sin B. Cross multiply:


33 sin B = 50 sin 132. Divide by 33 and you get





sin B = (50 sin 132) / 33 = 1.12





No angle has a sine over 1, so this is impossible: no solution.





Then do #3 like #1