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

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.