Question:
(i) In ∆ABC, ∠A = 90°. Which is its longest side?
(ii) In ∆ABC, ∠A = ∠B = 45°. Which is its longest side?
(iii) In ∆ABC, ∠A = 100° and ∠C = 50°. Which is its shortest side?
Solution:
(i) Given: In ∆ABC, ∠A = 90°
So, sum of the other two angles in triangle ∠B + ∠C = 90°
i.e. ∠B, ∠C < 90°
Since, ∠A is the greatest angle.
So, the longest side is BC.
(ii) Given: ∠A = ∠B = 45°
Using angle sum property of triangle,
∠C = 90°
Since, ∠C is the greatest angle.
So, the longest side is AB.
(iii) Given: ∠A = 100° and ∠C = 50°
Using angle sum property of triangle,
∠B = 30°
Since, ∠A is the greatest angle.
So, the shortest side is BC.