Question

In a right angled triangle, if one angle is ${30}^o$ then the side opposite to it is:

• A. one third of the base
• B. half of the hypotenuse
• C. one fourth of the hypotenuse
• D. one sixth of the hypotenuse

Answer 1

The correct option is B half of the hypotenuse

This is an $Equilateral$ triangle.

Let, the sides of $Equilateral$ triangle be $a$

The angles are all the same too, and since the angles must add up to ${180}^o$ we conclude that the three angles in the equilateral triangle are equal to $\frac{180}{3}={60}^o$

The angle at the bottom is ${90}^o$

One of the angles is the same as one of the angles in the original equilateral triangle, so it is ${60}^o$

So the third angle must be $180-90-60={30}^o$

Now the hypotenuse of this new triangle is $a$ and the side length of the equilateral triangle. And the length of the shortest side is $\frac{a}{2}$ i.e. $half$ of the $hypotenuse$ since the line we drew cut the bottom line in half.

18 we conclude that the three angles in the equilerl triangle are equal to180∘/