Question

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

Answer 1

In ∆FAN,

∠F + ∠A + ∠N = 180°     ...(sum of measures of angles of a triangle is 180°)

⇒ 80° + 40° + ∠N = 180°   

⇒ 120° + ∠N = 180°

⇒ ∠N = 180° − 120°

= 60°

Now, in △FAN, ∠F and ∠A are the largest and smallest angles.

The side opposite to the largest angle is the greatest side and the side opposite to the smallest angle is the smallest side.

Hence, the greatest and the smallest side of the triangle are AN and ​FN respectively.