What is the area of a parallelogram that has a 70 degree angle and sides with lengths 140 and 200?

The area of the parallelogram is

To find the area of a parallelogram given one angle and the lengths of two adjacent sides, you can use the formula:

[ \text{Area} = \text{base} \times \text{height} ]

Where the base is one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.

To find the height, you can use trigonometry. Since the given angle is 70 degrees and the adjacent side lengths are 140 and 200, the height can be found using the sine of the angle:

[ \text{height} = \text{side length} \times \sin(\text{angle}) ]

For the given problem:

[ \text{height} = 140 \times \sin(70^\circ) ]

[ \text{height} \approx 140 \times 0.9397 ]

[ \text{height} \approx 131.356 ]

Now, you can calculate the area using the base and height:

[ \text{Area} = 200 \times 131.356 ]

[ \text{Area} = 26271.2 ]

So, the area of the parallelogram is approximately 26271.2 square units.