Find the lengths of the missing sides in the triangle. Use the Triangle Theorem. Write your answers as integers, in radical form, or as decimals rounded to the nearest tenth. The diagram is not drawn to scale.
Since this is a right triangle, we can use the Pythagorean Theorem to find the missing side lengths.
Let's start by labeling the sides:
- The side opposite the 30-degree angle is 8 units
- The side opposite the 60-degree angle is the hypotenuse (which we'll call "c")
- The side opposite the right angle is the longest side, so it must be the hypotenuse
Now, we can use the Triangle Theorem. The sides of a 30-60-90 triangle are in the ratio 1 : $\sqrt{3}$ : 2.
Since the side opposite the 30-degree angle is 8 units, we can find the length of the hypotenuse:
c = 2 * 8 = 16 units
Therefore, the lengths of the missing sides are:
- The side opposite the right angle is 16 units
- The side opposite the 60-degree angle is also 16 units