Given right triangle xyz, if angle x is $30°$ and the length of the side opposite angle x is $5$, what is the length of the hypotenuse?

• A. $\frac{5}{\cos (30°)}$
• B. $\frac{5}{\sin (30°)}$
• C. $5\times \sin (30°)$
• D. $5\times \cos (30°)$

Answer: (B)

Verified step by step guidance

1. Identify the given information: angle \( x = 30^\circ \) and the length of the side opposite angle \( x \) is 5.
2. Recall the definition of sine in a right triangle: \( \sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}} \). Here, \( \theta = 30^\circ \).
3. Set up the equation using sine: \( \sin(30^\circ) = \frac{5}{\text{hypotenuse}} \).
4. Solve for the hypotenuse by multiplying both sides by the hypotenuse and then dividing both sides by \( \sin(30^\circ) \): \( \text{hypotenuse} = \frac{5}{\sin(30^\circ)} \).
5. Use the known value or a calculator to find \( \sin(30^\circ) \) if needed, but do not calculate the final numeric value unless asked.