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

30 in.

38 in.

40 in.

66 in.

38 in

Step-by-step explanation:

The remaining angle in the triangle formed by the two sides and the diagonal is ...

... 180° - 37°10' - 49°20' = 93°30'

The law of sines tells you the longest side (s) is opposite the largest of the given angles, so satisfies the proportion ...

... s/sin (49°20') = (50 in) / sin (93°30')

... s = (50 in) ·sin (49°20') / sin (93°30') ≈ 37.9966 in ≈ 38 in