Question

In right angle triangle, the side opposite to the angle having measure 30 is ................. to the hypotenuse

• A. three times
• B. half
• C. double
• D. fourth part

Answer 1

Answer: (B)

half

Let's take an equilateral triangle $ABC$

$⟹AB=BC=AC=a$ and $m\angle A=m\angle B=m\angle C={60}^o$

Let's draw an altitude from $A$ on $BC$ which bisects $BC$ at $D$ and also bisects angle $A$.

Then, we get a right angle triangle at $D,$ such that $m\angle DAB={30}^o$ and $DB=\frac{a}{2}$ is the side opposite to the angle of measure ${30}^o$

Now, length of hypotenuse $AB=a=2\times \frac{a}{2}=2DB$

$\therefore DB=\frac{1}{2}AB$

Hence, the side opposite to the angle having measure ${30}^o$ is half the length of the hypotenuse.