Answer:
Never.
Step-by-step explanation:
Definition:
In a 30-60-90 triangles:
- The length of a hypotenuse sides is twice the length of the shorter leg
- The length of the Longer side is \(\sqrt{3}\) times the shorter leg.
As per the statement:
In a 30-60-90 triangle the long leg is half the hypotenuse.
since,
\(\text{Shorter leg} = \frac{1}{\sqrt{3}} \cdot \text{Length of longer side}\)
By definition;
length of a hypotenuse sides is twice the length of the shorter leg
⇒\(\text{length of hypotenuse} = 2 \cdot \frac{1}{\sqrt{3}} \cdot \text{Length of longer side}\)
⇒\(\text{length of hypotenuse} =\frac{2}{\sqrt{3}} \cdot \text{Length of longer side}\)
⇒\(\text{length of longer side} =\frac{\sqrt{3}}{2} \cdot \text{Length of Hypotenuse side}\)
Therefore. the given statement "In a 30-60-90 triangle the long leg is half the hypotenuse." is Never.
