Given a right triangle where one of the acute angles is $30°$ and the hypotenuse is $10$, what is the length of the side opposite the $30°$ angle (let this length be $x$)?

• A. $10$
• B. $7$
• C. $8.66$
• D. $5$

Answer: (D)

Verified step by step guidance

1. Identify the given information: a right triangle with one acute angle measuring 30° and the hypotenuse length of 10.
2. Recall the special property of a 30°-60°-90° right triangle: the side opposite the 30° angle is exactly half the length of the hypotenuse.
3. Set the length of the side opposite the 30° angle as \(x\) and write the relationship using the property: \(x = \frac{1}{2} \times \text{hypotenuse}\).
4. Substitute the given hypotenuse length into the equation: \(x = \frac{1}{2} \times 10\).
5. Simplify the expression to find the length of the side opposite the 30° angle (do not calculate the final value here, just set up the expression).