In circle O, ST is a diameter. If angle S measures $22.0°$, angle T measures $25.0°$, and angle O measures $25.4°$, what must be the value of x using the Law of Sines?

• A. $37.2$
• B. $25.4$
• C. $22.0$
• D. $25.0$

Answer: (B)

Verified step by step guidance

1. Identify the triangle involved in the problem and label the vertices and angles clearly. Since ST is a diameter of circle O, triangle SOT or TOT (depending on the points) is inscribed in the circle with ST as the diameter.
2. Recall that the angle subtended by a diameter in a circle is a right angle (90 degrees). This means the angle opposite the diameter ST is 90 degrees.
3. Use the given angle measures (22.0°, 25.0°, and 25.4°) to determine which angles correspond to which vertices in the triangle. Confirm that the sum of the angles in the triangle is 180 degrees.
4. Apply the Law of Sines, which states that for any triangle with sides a, b, c opposite angles A, B, C respectively, the ratio \( \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \) holds true.
5. Set up the Law of Sines equation using the known angles and sides, then solve for the unknown value x by isolating it in the equation.