Question

question 6 of 12 knowing that sin 30° = 1/2, what is a? a. 18 b. 15.59 c. 9 d. 4.5

Explanation:

Step1: Identify triangle type

Right triangle with 30°, 60°, 90° angles.

Step2: Relate sides to angles

Side opposite 60° is \( a \), adjacent to 30° is 9 (hypotenuse \( c \)).

Step3: Use cosine of 30°

\(\cos 30^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{9}{c}\), \(\cos 30^\circ = \frac{\sqrt{3}}{2}\).

Step4: Solve for hypotenuse \( c \)

\( c = \frac{9}{\cos 30^\circ} = \frac{9}{\sqrt{3}/2} = \frac{18}{\sqrt{3}} = 6\sqrt{3} \).

Step5: Find \( a \) (opposite 60°)

\(\sin 60^\circ = \frac{a}{c}\), \( a = c \cdot \sin 60^\circ = 6\sqrt{3} \cdot \frac{\sqrt{3}}{2} = 9\sqrt{3} \approx 15.59 \).

Answer:

B. 15.59