Problem solving

Question

Two adjacent sides of a parallelogram are 3473' and 4822', respectively. The angle between these two sides is 72.32 degrees. Find the length of the longer diagonal. I got 5009.11, but it is wrong. Was I wrong to use the law of cosines or did I calculate wrong or did I use the wrong numbers?

Answer 1

The first answer to this question is actually incorrect. It finds the length of the shorter diagonal of the parallelogram instead of the longer diagonal. The longer diagonal is always across from the parallelogram's largest angle (that is, it runs between the vertices of the two small angles).

 

You'll want to find the parallelogram's other angle measure, which is supplementary to the angle you were given:

 

180º - 72.32º = 107.68º

 

Now, use the law of cosines with that angle measure instead to find the length of the diagonal across from the larger angle:

 

d² = 3473² + 4822² - 2(3473)(4822)cos(107.68)

d² = 12061729 + 23251684 - (33493612)cos(107.68)

d² = 35313413 - (-10172026.7)

d² = 35313413 + 10172026.7

d² = 45485439.7

d = 6,744.29 feet

Answer 2

using the law of cosines...

d²=3473²+4822²-2(3473)(4822)(cos[72.32])

d²=12,061,729+23,251,684-2(16,746,806)(0.3037005)

d²=35,313,413-(33,493,612)(0.3037005)

d²=35,313,413-10,172,027

d²=25,141,386

d=5014.118 feet