Question

In a 30-60-90 triangle the long leg is half the hypotenuse
Always
Sometime
Never

Answer 1

I wanted to say Sometime
But I believe the answer is Never

Answer 2

Never.

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
  `√(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} = (1)/(√(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 (1)/(√(3)) \cdot \text{Length of longer side}`

⇒
`\text{length of hypotenuse} =(2)/(√(3)) \cdot \text{Length of longer side}`

⇒
`\text{length of longer side} =(√(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.