SOLUTION: The legnths of two adjacent sides of a parallelogram are 6 and 15. If the measure of an included angle is 60 degrees. What is the legnth of the shorter diagnol of the parallelogram

Question 67447: The legnths of two adjacent sides of a parallelogram are 6 and 15. If the measure of an included angle is 60 degrees. What is the legnth of the shorter diagnol of the parallelogram?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The lengths of two adjacent sides of a parallelogram are 6 and 15. If the measure of an included angle is 60 degrees. What is the length of the shorter diagonal of the parallelogram?
:
We know the short diagonal is opposite the smaller angle, in this case it's 60 deg
:
Draw the triangle, Let A = 60 degrees, the diagonal = a, b = 15, c = 6
:
We have side-angle-side here which lends itself to the law of cosines:
a^2 = b^2 + c^2 - 2(b*c)cos(A)
:
a^2 = 15^2 + 6^2 - 2(15*6)Cos(60)
:
a^2 = 225 + 36 - 2(90)(.5)
:
a^2 = 261 - 90
:
a = SqRt(171)
:
a = 13.1 is the length of the shorter diagonal
;

RELATED QUESTIONS
The adjacent sides of a parallelogram measure 8 by 6 inches. Their included angle is 45... (answered by Theo)

Two adjacent side of a parallelogram are 10 and 8 in. The included angle is 30 degrees.... (answered by FrankM)

If the sides of a parallelogram and an included angle are 5 ft, 10ft, 100 degrees,... (answered by josgarithmetic)

What is the are of a regular octagon of sides 8cm and included angle of 60... (answered by Alan3354)

Find the length of the longer diagonal of a parallelogram two of whose sides are 34mm and (answered by Edwin McCravy)

Parallelogram ABCD has one interior angle measuring 60�. What is the measure of the... (answered by jim_thompson5910)

How do you find the area of a parallelogram with sides 8 and 14 and an included angle of... (answered by richwmiller)

A parallelogram has sides of legnths of 3 and 5, and one angle is 50'. find the lengths... (answered by Edwin McCravy)

Find the area of a parallelogram with sides 10 feet and 40 feet and an included angle of... (answered by hokies)