Question

The diagonals of a parallelogram are 38 inches and 46 inches and intersect at an angle of 40 degrees. Find the length of the longer side. Round to the nearest whole number.

Answer 1

The length of the longer side of the parallelogram is 59 inches.

Step-by-step explanation:

The diagonals of a parallelogram form two congruent triangles. Using the law of cosines, we can determine the length of the longer side of the parallelogram.

Let's call the longer side 'a' and the lengths of the diagonals 'd1' and 'd2'. The formula is:

a = sqrt(d1^2 + d2^2 - 2 * d1 * d2 * cos(angle))

Plugging in the given values, we get:

a = sqrt(38^2 + 46^2 - 2 * 38 * 46 * cos(40°))

Calculating this gives us approximately 59 inches. Rounding to the nearest whole number, the length of the longer side is 59 inches.