Given a right triangle where one angle measures 60 degrees and the adjacent side to this angle is 12 units long, find the length of the hypotenuse.

In a right triangle, you can use the cosine function to find the length of the hypotenuse. Since you have one angle measuring 60 degrees and the adjacent side (which we'll call \( a \)) is 12 units long, you can use the relationship: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}. \] For a 60-degree angle, the cosine is: \[ \cos(60^\circ) = \frac{1}{2}. \] Plugging your values into the formula, you get: \[ \frac{1}{2} = \frac{12}{\text{hypotenuse}}. \] To find the hypotenuse (which we will call \( c \)), rearranging gives: \[ \text{hypotenuse} = \frac{12}{\frac{1}{2}} = 12 \times 2 = 24. \] Thus, the length of the hypotenuse is 24 units.