# Stuck on a question

• May 28th 2009, 08:24 PM
waxer1987
Stuck on a question
Hey, I have a trig question that I am stuck on and would appreciate any help, Thanks.
Two sides of a parallelogram measure 7.0 cm and 9.0 cm. The longer
diagonal is 12.0 cm long.
a) calculate all the interior angles.
b) How long is the other diagonal?

The answer page got for a) 96 and 84 degrees. for b) 10.8cm

I got the correct degrees, but I can't get 10.8cm.
• May 28th 2009, 08:35 PM
amitface
Use Law of Cosines with side lengths 7 and 9, and angle measure 84 deg.

(Make sure your calculator is in degrees)
• May 28th 2009, 08:57 PM
waxer1987
I used the cosine law, maybe i'm doing it wrong. This is what I did.

my sketch

A------------------D For some reason I can't draw the pic , but D and C are connected as well as A and B. (parrallelogram)
/ /
/ /7cm
/ /
B-----------------C
9cm

With a line from A to C which is 12.0cm.
And a line from B to D which I need to figure out.

I used Angle BDC

c^2 = b^2 + d^2 - 2bd cosC
144 = 130 - 126cosC
130-144 = -126cosC
-14 = -126cosC
-14/-126 = cosC
0.1111... = cosC
c= cos^-1(0.1111...)
c= 83 degrees

but how can it be 83 degrees if its obtuse? what did i do wrong? did I draw it wrong?
• May 28th 2009, 11:08 PM
VonNemo19

You've got a,b, and c. all you have to do is solve this for $\arccos(\gamma)$

The fact that a parrallelogram is $360degrees$ should do the rest.
• May 28th 2009, 11:59 PM
Cosine Rule
Hello waxer1987
Quote:

Originally Posted by waxer1987
I used the cosine law, maybe i'm doing it wrong. This is what I did.

my sketch

A------------------D For some reason I can't draw the pic , but D and C are connected as well as A and B. (parrallelogram)
/ /
/ /7cm
/ /
B-----------------C
9cm

With a line from A to C which is 12.0cm.
And a line from B to D which I need to figure out.

I used Angle BDC

c^2 = b^2 + d^2 - 2bd cosC
144 = 130 - 126cosC
130-144 = -126cosC Should be 144 - 130 = -126 cos C
-14 = -126cosC
-14/-126 = cosC
0.1111... = cosC
c= cos^-1(0.1111...) So cos C = -0.1111...
c= 83 degrees C = 96 degrees

but how can it be 83 degrees if its obtuse? what did i do wrong? did I draw it wrong?

I've corrected your mistake. So the acute angles are both $84^o$ (to the nearest degree).

For the shorter diagonal, use the acute angle in the Cosine Rule:

$a^2 = 130 - 126 \cos 83.6^o$

$= 116$

$\Rightarrow a = 10.8$