In Δ ABC, if ∠A=40° and ∠B=60°. Determine the longest and shortest sides of the triangle.
Given that in Δ ABC
∠A = 40o and ∠B = 60o
We have to find shortest and longest side.
We know that,
Sum of angles of triangle = 180o
∠A + ∠B + ∠C = 180o
40o + 60o + ∠C = 180o
100o + ∠C = 180o
∠C = 180o – 100o
= 80o
Now,
40o < 60o < 80o
∠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.