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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 triangle180°
⇒∠A+∠B+∠C=180°
⇒40°+60°+∠C=180°
⇒∠C=180° -(40° +60° )
=180° -100° =80°
∴∠C = 80°
Now,
⇒ 40<60<80⇒∠A< ∠B < ∠C
⇒ ∠Cis 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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