In Δ DEF, the lengths of sides DF : DE : EF = 11 : 5 : 12. Which is the smallest angle of the triangle?

Answer 1

use the Law of Cosine

c^2 = a^2 +b^2 -2abCosC

5^2 = 11^2 +12^2 -2(11)(12)CosC

CosC = (25-265)/-264 = 10/11

C = Cos^-1(10/11)

C = about 24.62 degrees

the smallest angle is the angle opposite the smallest side, so you know C<60

and maybe <60/2 <30 as 5 < half of either of the other sides