The lengths of the diagonals of a parallelogram are 20 inches and 30 inches. The diagonals intersect at an an angle 35 degrees. Find the lengths of the parallelogram's sides lengths to the nearest hundredth.
To find the lengths of the parallelogram's sides, we can use the formula:
\(a = \sqrt{d_1^2 + d_2^2 - 2 \cdot d_1 \cdot d_2 \cdot \cos(\theta)}\)
where:
\(a\) = length of one side of the parallelogram
\(d_1\) = length of one diagonal
\(d_2\) = length of the other diagonal
\(\theta\) = angle between the diagonals
Given:
\(d_1\) = 20 inches
\(d_2\) = 30 inches
\(\theta\) = 35 degrees
Substituting the given values into the formula, we have:
\(a = \sqrt{20^2 + 30^2 - 2 \cdot 20 \cdot 30 \cdot \cos(35)}\)
Now, let's calculate this expression and find the value of side \(a\).