Question:
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
Solution:
Given that in ΔABC, ∠A = 40° and ∠B = 60°
We have to find longest and shortest side
We know that,
Sum of angles in a triangle 180°
∠A + ∠B + ∠C = 180°
40° + 60° + ∠C = 180°
∠C = 180° - ((10)0°) = 80°
∠C = 80°
Now,
⟹ 40° < 60° < 80° = ∠A < ∠B < ∠C
⟹ ∠C is greater angle and ∠A is smaller angle.
Now, ∠A < ∠B < ∠C
⟹ BC < AAC < AB [Side opposite to greater angle is larger and side opposite to smaller angle is smaller]
AB is longest and BC is smallest or shortest side.
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