Question

Two adjacent sides of a parallelogram

are 3473' and 4822', respectively. The
angle between these two sides is 72.23º.
Find the length of the longer diagonal.
D
4822
3473
b
a
A
72.23
C
B
Round to the nearest foot.
Enter​

Answer 1

6748'

Explanation:

The long diagonal is the third leg of a triangle with the given side lengths and an angle between them that is the supplement of the given angle. Its length can be found from the Law of Cosines.

a^2 = b^2 +c^2 -2bc·cos(A)

a^2 = 3473^2 +4822^2 -2·3473·4822·cos(180° -72.23°)

a^2 = 45,535,553.83

a ≈ 6748.004

The longer diagonal is about 6758 feet long.