Triangles

It is the 30-60-90 triangle with ratio $1:\sqrt{3}:2$

Let the smallest acute angle be $x$ . Then,

$90^\circ + x + 2x = 180^\circ$

Solving this, we get $x = 30^\circ$ .

This problem is the exact statement of $30^\circ - 60^\circ - 90^\circ$ theorem which states that if in a triangle, the angles are $30^\circ, 60^\circ,$ & $90^\circ$ , then the hypotenuse is twice the shortest side.

If we solve a simultaneous equation that is related to the angle of the right triangle, then we get $x + y = 180 - 90, x = 2y$ .

Then, we get $x = 60, y = 30$ .

This problem is related to trigonometric functions, but we do not have to know that.

If each angle of the triangle is $30, 60, 90$ , then the length of the hypotenuse is double of its shortest side.

Then, the correct answer is $\boxed { \text { Double the smallest side } }$ .

PS: It is not the 'smallest'. In the geometrical works, we don't say 'the smallest' because the side cannot be the smallest. We say 'shortest' instead.

Apply the 30-60-90 special right triangle

"the longer leg is square root of 3 times as long as the shorter leg while the hypotenuse is twice as long as the shorter leg"