To find the area of the triangle in the image, we can use the following formula for the area of a triangle when two sides and the included angle are known:

$\text{Area} = \frac{1}{2} \times a \times b \times \sin(C)$

Where:

• $a = 3$ (one side of the triangle),
• $b = 5$ (another side of the triangle),
• $C = 30^\circ$ (the angle between these two sides).

Now, we can calculate the area by plugging these values into the formula. The sine of $30^\circ$ is $\frac{1}{2}$.

$\text{Area} = \frac{1}{2} \times 3 \times 5 \times \sin(30^\circ)$ $\text{Area} = \frac{1}{2} \times 3 \times 5 \times \frac{1}{2}$ $\text{Area} = \frac{1}{2} \times 7.5 = 3.75$

So, the area of the triangle is 3.75. The correct answer is the second option: 3.75.

Would you like more details on this or have any further questions?

Here are five related questions you might find interesting:

1. How do you calculate the area of a triangle using different sets of known values?
2. What is the Law of Sines and how can it be applied in triangle problems?
3. How do trigonometric ratios help in solving triangle-related problems?
4. Can we calculate the height of the triangle using the given information?
5. What are the common formulas for calculating the area of a triangle?

Tip: Always make sure you have the correct angle's sine value when using trigonometric functions in geometry.