ABC is a right angled triangle whose hypotenuse is AC. If AB : BC = 3 : 4, then the smallest angle of the triangle is :

1. ∠A

2. ∠B

3. ∠C

4. None of these

In △ABC,

Given,

AB : BC = 3 : 4

Let, AB = 3x and BC = 4x

By pythagoras theorem,

⇒ AC² = AB² + BC²

⇒ AC² = (3x)² + (4x)²

⇒ AC² = 9x² + 16x²

⇒ AC² = 25x²

⇒ AC = $\sqrt{25\text{x}^2}$

⇒ AC = 5x.

We know that,

The shortest angle of a triangle has the shortest side opposite to it.

Since, side AB is shortest, thus ∠C is the shortest angle.

Hence, option 3 is the correct option.