Question

fall 2025 geometry b wvva right triangle relationships and trigonometry given right triangle qrs, what is the value of sin(30°)?

Explanation:

Step1: Recall sine - angle relationship

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for $\theta = 30^{\circ}$

In a right - triangle, for an angle of $30^{\circ}$, if the hypotenuse is $c$ and the side opposite the $30^{\circ}$ angle is $a$.

Step3: Use the special right - triangle ratio

In a $30 - 60-90$ right - triangle, if the hypotenuse $c$ and the side opposite the $30^{\circ}$ angle $a$, the ratio of the side opposite the $30^{\circ}$ angle to the hypotenuse is $\sin(30^{\circ})=\frac{1}{2}$.

Answer:

$\frac{1}{2}$