A 30-60-90 triangle drawn inside the unit circle intersects that unit circle at point (x,y)

Question

. What is the length of the hypotenuse of this triangle?(1 point)

Answer 1

In a 30-60-90 triangle, the angles are \(30^\circ\), \(60^\circ\), and \(90^\circ\). The side lengths have a specific ratio:

• The side opposite the \(30^\circ\) angle is \( \frac{1}{2} \) the length of the hypotenuse.
• The side opposite the \(60^\circ\) angle is \( \frac{\sqrt{3}}{2} \) the length of the hypotenuse.

Since we are considering a triangle inscribed in the unit circle, the hypotenuse of this triangle will coincide with the radius of the unit circle, which is always 1.

Thus, the length of the hypotenuse of the 30-60-90 triangle drawn inside the unit circle is:

\[ \boxed{1} \]