Question

If the angles of a triangle are ${30}^o,{60}^o$ and ${90}^o$, then what is the ratio of the sides opposite to these angles?

• A. $\sqrt{3}:\sqrt{2}:1$
• B. $1:\sqrt{2}:2$
• C. $2:\sqrt{3}:1$
• D. $3:2:1$

Answer 1

The correct option is C $2:\sqrt{3}:1$

The property is that the lengths of the sides of a 30-60-90 triangle are in the ratio 1:2:√3. Thus if you know that the side opposite the 60 degree angle measures 5 inches then then this is √3 times as long as the side opposite the 30 degree so the side opposite the 30 degree angle is 5/√3 inches long

So option C is the correct answer.