Question

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.

Answer 1

38 in

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