A diagonal of a parallelogram is 50 inches long and makes angles of 37°10' and 49°20' with the sides. Solve for the longest side of the parallelogram.

Angles of the parallelogram:

α = 49° 20' + 37° 10' = 86° 30'

β = 180° - 86° 30' = 93° 30'

x - length of the longest side of the parallelogram;

The Sine Law:

x / sin 49°30' = 50 / sin 93°30'

x / 0.7585 = 50 / 0.998

0.998 x = 37.925

x = 37.925 : 0.998

x = 38 in

Answer:

The longest side of the parallelogram is 38 inches long.