given that sides of a triangle are in the ratio of 3: 5：6：find the angles of the triangle

Answer 1

3/sinA = 5/sinB = 6/sinC law of sines

6^2 = 3^2 + 5^2 -2(3)(5)cosC law of cosines

30cosC = 9+25 -36 = -2

cosC =-2/30

C=-1/15 = 180-86.2 = 93.8 degrees

3/sinA = 6/sin93.8 = 6.013

sinA = 3/6.013 = .4989

A = 29.9 degrees

B = 180-93.8-29.9 = 56.3 degrees

sin56.3 = 0.832

5/.832 = 6.01 = 3/sinA = 6/sinC

A= 29.9, the angle opposite the shortest side

C= 93.8, the angle opposite the longest side

B = 56.3, the angle opposite the middle length side

It's close to a 30-60-90 right triangle. 6^2 almost equaled 3^2 + 5^2 36 was close to 34