In Δ ABC, if ∠A=40° and ∠B=60° . Determine the longest and shortest sides of the triangle.

Given that in Δ ABC

∠A = 40^o and ∠B = 60^o

We have to find shortest and longest side.

We know that,

Sum of angles of triangle = 180^o

∠A + ∠B + ∠C = 180^o

40^o + 60^o + ∠C = 180^o

100^o + ∠C = 180^o

∠C = 180^o – 100^o

= 80^o

Now,

40^o < 60^o < 80^o

∠A < ∠B < ∠C

∠C is greater angle and ∠A is smaller angle.

As, ∠A < ∠B < ∠C

BC < AC < AB (Therefore, side opposite to greater angle is larger and side opposite to smaller angle is smaller)

Therefore, AB is longest, and BC is smallest or shortest side.