Question

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.

Answer 1

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.