Question

Using $30-60-90$ degree triangle theorem, find the shortest and longest side of the given triangle.

• A. shortest side $=1$, longest side $=$ $\sqrt{3}$
• B. shortest side $=2$, longest side $=$ $\sqrt{3}$
• C. shortest side $=1$, longest side $=$ $2\sqrt{3}$
• D. shortest side $=1$, longest side $=$ $\sqrt{2}$

Answer 1

The correct option is A shortest side $=1$, longest side $=$ $\sqrt{3}$

Using $30-60-90$ degree triangle theorem, the sides are in the ratio $1:2:$ $\sqrt{3}$
Shortest side $=$ $\frac{1}{2}\times$ hypotenuse
Longest side $=$ $\frac{1}{2}\sqrt{3}\times$ hypotenuse
So, the shortest side or adjacent side $=$ $\frac{1}{2}\times 2$ $=1$
Longest side $=$ $\frac{1}{2}\times 2\sqrt{3}=\sqrt{3}$