What is the area of the triangle?

Calculation:

Given,

The sides of the triangle are: a = 5 cm, c = 3 cm, and the angle B = \(120^\circ \) between sides a and c.

The area of the triangle is given by the formula:

\( \text{Area} = \frac{1}{2} \times a \times c \times \sin B \)

\( \text{Area} = \frac{1}{2} \times 5 \times 3 \times \sin(120^\circ) \)

We know that\(\sin(120^\circ) = \frac{\sqrt{3}}{2} \), so:

\( \text{Area} = \frac{1}{2} \times 5 \times 3 \times \frac{\sqrt{3}}{2} \)

\( \text{Area} = \frac{1}{2} \times 15 \times \frac{\sqrt{3}}{2} = \frac{15 \times \sqrt{3}}{4} \)

∴ The area of the triangle is \(\frac{15\sqrt{3}}{4} \) square cm.

Hence, the Correct answer is Option 1.