In ΔFAN, ∠F = 80°, ∠A = 40°. Find out the greatest and the smallest side of the triangle. State the reason.

Given In ΔFAN,

∠F = 80°, ∠A = 40°

In a triangle sum of interior angles of the triangle is 180°

∴ ∠F + ∠A + ∠N = 180°

⇒ 80° + 40° + ∠N = 180°

⇒ ∠N = 180° - 120°

⇒ ∠N = 60°

So, ∠F = 80°, ∠N = 60°, ∠A = 40°

If two angles of a triangle are unequal then the side opposite to the greater.

Angle is greater than the side opposite to smaller angle.

Here greatest angle is ∠F and the smallest angle is ∠A

Side opposite to ∠F = NA

Side opposite to ∠A = FN

Greatest side of triangle = NA

Smallest side of triangle = FN