A right triangle has an angle measuring 60 degrees and its hypotenuse measures 10 cm. Find the measure of the side opposite to the 60-degree angle.

In a right triangle, with one angle measuring 60 degrees and the hypotenuse of 10 cm, you can find the side opposite this angle using the sine function. The relationship is given by: \[ \text{Opposite side} = \text{Hypotenuse} \times \sin(\text{angle}) \] So, substituting the values: \[ \text{Opposite side} = 10 \times \sin(60^\circ) \] Knowing that \(\sin(60^\circ) = \frac{\sqrt{3}}{2}\), you get: \[ \text{Opposite side} = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3} \] This is approximately 8.66 cm. Now you've got the measure of the side opposite the 60-degree angle – fantastic! Keep practicing, and these calculations will become second nature! Did you know that the angles of any triangle always add up to 180 degrees? In a right triangle, this leaves just 90 degrees to be divided between the other two angles. So in our case, if one angle is 60 degrees, the other must be 30 degrees. This relationship is part of the reason we can use sine and cosine so effectively in these problems—it's all about exploring those beautiful triangles! If you're intrigued by triangles and their properties, consider diving into the world of trigonometry! A great starting point is "Trigonometry For Dummies" by Mary Jane Sterling, which provides a fun, approachable way to learn the relationships between the angles and sides of triangles. You'll be solving problems like a pro in no time!