Question

The sides of a parallelogram have lengths of 12 in and 26 in and one angles of 62 degrees. Find the length of the longer diagonal.

Answer 1

help please!

Answer 2

first, we are going to label everything.

Answer 3

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l l
l l
l l
l_____________________l

Answer 4

i called the parallelogram ABCD and drew a line from edge to edge so that it looked like 2 triangles. i used the law of cosines to find the third side and i got 22.96 but that doesn't correspond to my teachers answer, 44.6. what did i do wrong?

Answer 5

We are going to find the length of the longest diagonal. So, in order find it, find first the angle consecutive to 62 degrees. And it is 118 degrees.
Use the Law of Cosines.
We will represent the longer diagonal as X.
\[x ^{2}=12^{2}+26^{2}-2(12)(26)\cos (118 degrees)\]
\[x ^{2}=144+676-(-292.95)\]
\[x ^{2}=820+292.95\]
\[x ^{2}=1,112.95\]
x=33.36

Answer 6

my teachers answer was 44.6 so which answer
is right and which one is wrong?

Answer 7

i think my answer is correct.

Answer 8

ok thanks

Answer 9

get it?

Answer 10

yeah i do get it but um how did you know to make the angle 118 degrees instead of 62 degrees when you use law of cosines

Answer 11

ohh 180-62 degrees. never mind sry

Answer 12

simple. As we all know the two consecutive angles of a parallelogram sums up to 180 degrees. So, just subtract 62 to 180. Thus, getting 118 degrees. We are going to get the angle to use the Law of Cosines with the Case Given two sides and the included angle.

Answer 13

yeah i answered my own question after i posted it. sry about that. thanks for the help.

Answer 14

you are welcome. I checked my answer and it will still give the answer that i posted.