The lengths of the diagonals of a parallelogram are 20 inches and 30 inches. The diagonals intersect at an angle of 35 degrees. Find the lengths of the parallelograms sides to the nearest hundredth.
wda
To find the lengths of the sides of the parallelogram, we can use the formula:
l^2 = d1^2 + d2^2 - 2 * d1 * d2 * cosθ
where:
- l is the length of one side of the parallelogram
- d1 and d2 are the lengths of the diagonals of the parallelogram
- θ is the angle between the diagonals
Let's substitute the given values into the formula:
l^2 = 20^2 + 30^2 - 2 * 20 * 30 * cos35°
Now we can calculate it:
l^2 = 400 + 900 - 2 * 20 * 30 * cos35°
l^2 = 1300 - 1200 * cos35°
Using a calculator, evaluate cos35°:
cos35° ≈ 0.819152044
l^2 = 1300 - 1200 * 0.819152044
l^2 = 1300 - 983.3824528
l^2 ≈ 316.6175472
Now, to find the length of each side, we take the square root of both sides:
l ≈ √316.6175472
l ≈ 17.78
Therefore, the lengths of the parallelogram's sides are approximately 17.78 inches.
the diagonals bisect each other
use the law of cosines to find the sides