Question

A ceramic tile is in the shape of a triangle. The angle measurements of this triangle are 30 degrees, 60 degrees, and 90 degrees. The leg across from the 30 degree angle is 6.25 cm long. How long is the hypotenuse of this triangle?

Answer 1

Ratio of 30-60-90 triangles in terms of side lengths is 1-$\sqrt{3}$-2

So, the side across the 30-degree angle is 6.25.
Thus, the side across the 90-degree angle (hypotenuse) is 12.5.

Answer 2

A 30 60 90 triangle is a special triangle that has simple proportions for it's side lengths. The short leg to long leg ratio is 1:sqrt(3); the short leg to hypotenuse ratio is 1:2. If the length of the short leg (across from the 30 degree angel) is 6.25 cm long, then the length of the hypotenuse is twice that: 12.5 cm.