A right triangle has a hypotenuse of length $10$ units and one of its acute angles measures $30°$. What is the length of each leg of the triangle?

• A. The legs have lengths $7$ units and $7$ units.
• B. The legs have lengths $6$ units and $8$ units.
• C. The legs have lengths $10$ units and $10$ units.
• D. The legs have lengths $5$ units and $5\surd 3$ units.

Answer: (D)

Verified step by step guidance

1. Identify the given information: the hypotenuse length is 10 units, and one acute angle is 30° in a right triangle.
2. Recall the properties of a 30°-60°-90° right triangle: the sides are in the ratio 1 : \sqrt{3} : 2, where the hypotenuse corresponds to 2.
3. Set up the proportion using the hypotenuse: if the hypotenuse is 10 units, then the side opposite 30° (the shorter leg) is half the hypotenuse, so calculate it as \(\frac{10}{2}\).
4. Calculate the length of the other leg (opposite 60°) using the ratio: multiply the shorter leg by \(\sqrt{3}\) to find the longer leg.
5. Express the lengths of the legs as \$5\( units and \)5\sqrt{3}$ units, corresponding to the sides opposite 30° and 60°, respectively.