We are given a parallelogram with one side of length 10 m, an adjacent side of length 8 m, and the angle between them is 60 degrees. We want to find the area of the parallelogram.

1. Problem Description

We are given a parallelogram with one side of length 10 m, an adjacent side of length 8 m, and the angle between them is 60 degrees. We want to find the area of the parallelogram.

2. Solution Steps

We can find the height $h$ of the parallelogram by using the sine function. We have

$$\sin(60^{\circ}) = \frac{h}{8}$$

Thus, $h = 8 \sin(60^{\circ})$. We know that $\sin(60^{\circ}) = \frac{\sqrt{3}}{2}$.

$$h = 8 \cdot \frac{\sqrt{3}}{2} = 4\sqrt{3}$$

The area of a parallelogram is given by the formula $A = b \cdot h$, where $b$ is the base and $h$ is the height.

In this case, the base is 10 m and the height is $4\sqrt{3}$ m. Therefore, the area is

$$A = 10 \cdot 4\sqrt{3} = 40\sqrt{3}$$

$40\sqrt{3} \approx 40 \times 1.732 = 69.28$

3. Final Answer

The area of the parallelogram is $40\sqrt{3} \ m^2$.