22.2k views
0 votes
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​

User Augustss
by
8.5k points

1 Answer

3 votes

Answer:

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.

User RedMage
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.