the angles of triangle abc are in the ratio of 1:3:8. The ratio of the longest side of the triangle to the next longest side is

Question

A) 8:3

B) Radical 2: 1

C)2: Radical 3

D) Radical 6: 2

E) Radical 8: Radical 3

Answer 1

The angles of the triangle are 15 deg, 45 deg, and 120 deg.  The ratio of the angles is 1:3:8.  According to the Law of Sines, the ratio of the sides are sin (15) : sin (45) : sin (120).  The ratio of the longest side to the next longest side will be (√3 /2) : (√2 / 2) = √3 / √2 = √6 / 2.

 

Answer 2

Angle 8 is the longest angle because it is the largest number in the ratio.  Angle 3 is the second longest angle because it is the second largest number in the ratio.  Angle 8 is opposite to side 8.  Angle 3 is opposite to side 3.  So the ratio of the longest side to next longest side is

 

8:3