Question

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

 

Answer 1

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.