A diagonal of a parallelogram is 20 inches long and makes angles of 17° and 49° with the sides. How long is the longest side?

Angles of the parallelogram which is given in the problem are:α = 49° + 17 ° = 66°

β = 180° - 66° = 114°

x - length of the longest side of the parallelogram;

Use the Sine Law:x / sin 49° = 20 / sin 17°

x / 0.7547 = 20 / 0.2924

0.2924 x = 15.094

x = 15.094 :.2924

x = 51.62 is the longest side of the parallelogram.