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?

Answer 1

(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.