Question

$\text{(i) In}\Delta ABC,\angle A={90}^{\circ }.\text{Which is its longest side?}\text{(ii)IN}\Delta ABC,\angle A=\angle B={45}^{\circ }.\text{Which is its longest side?}\text{(iii) In}\Delta ABC,\angle A={100}^{\circ }and\angle C={50}^{\circ }.\text{Which is its shortest side?}$

Answer 1

(i) Given: In ∆ ABC, ∠ A = 90°
So, the 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 a 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 a triangle,
∠ B = 30°
Since ∠ B is the shortest angle.
So, the shortest side is AC.