find measurement of c,ab,and ac

Question

Sol1 : m∠C =  °, AB = , AC = 

Sol2 : m∠C =  °, AB = , AC = 

Sol3 : m∠C =  °, AB = , AC = 

Answer 1

The angles in a triangle add up to 180°, so m∠C = 180° - 93° - 14° = 73°. For the sides AB and AC, use the Law of Sines:

BC/sin(A) = AC/sin(B) = AB/sin(C)

You know the first one is BC/sin(A) = 52/sin(93). To find AC:

52/sin(93) = AC/sin(14)

52·sin(14)/sin(93) = AC

Use your calculator to get the answer. To find AB:

52/sin(93) = AB/sin(73)

52·sin(73) / sin(93) = AB

Again, use your calculator to get the answer.