Question

Two sides of a parallelogram are 32 feet and 77 feet. The measure of the angle between these sides is 16°. Find the area of the parallelogram to the nearest square foot.

Answer 1

The area of the parallelogram is approximately 277.44 square feet.

Step-by-step explanation:

To find the area of a parallelogram, we can use the formula: Area = base * height. In this case, the two given sides of the parallelogram are the base and the height.

Given that the two sides are 32 feet and 77 feet, and the angle between them is 16°, we can use trigonometry to find the height of the parallelogram.

By using the sine function, we can determine that the height is given by the equation: height = side * sin(angle).

Plugging in the values, we get: height = 32 * sin(16°) = 8.62 feet (rounded to two decimal places).

Now we can calculate the area: Area = 32 * 8.62 = 277.44 square feet (rounded to the nearest square foot).