Questions: Solve with simplifying your answer including any radical. Use integers or Fractions b=3 sin(60°)

Solution Steps

To solve for \( b \) given \( b = 3 \sin(60^\circ) \), we need to:

1. Recognize that \( \sin(60^\circ) \) is a known trigonometric value.
2. Use the exact value of \( \sin(60^\circ) \), which is \( \frac{\sqrt{3}}{2} \).
3. Multiply 3 by \( \frac{\sqrt{3}}{2} \) to get the simplified answer.

The sine of \( 60^\circ \) is a known trigonometric value: \[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \]

Substituting this value into the equation for \( b \): \[ b = 3 \sin(60^\circ) = 3 \left(\frac{\sqrt{3}}{2}\right) \] This simplifies to: \[ b = \frac{3\sqrt{3}}{2} \]

Calculating the decimal value of \( b \): \[ b \approx 2.5981 \]

Final Answer