# Math Help - parallelogram problem

1. ## parallelogram problem

Tried more than twice for this problem to get D as the answer. Only to find out that B is the correct answer (according to my instructor). Could someone help me out in explaining why B is the answer. I thought this was just another Cosine Law problem.

PROBLEM:
A side and diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side is 124 degrees. Find the length of the other diagonal.

a. 7.73 b. 7.48 c. 7.84 d. 7.94

THANKS !!!

2. Originally Posted by killykilly
Tried more than twice for this problem to get D as the answer. Only to find out that B is the correct answer (according to my instructor). Could someone help me out in explaining why B is the answer. I thought this was just another Cosine Law problem.

PROBLEM:
A side and diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side is 124 degrees. Find the length of the other diagonal.

a. 7.73 b. 7.48 c. 7.84 d. 7.94

THANKS !!!
1. Draw a sketch.

2. Use the Sine rule to calculate $\alpha$:

$\dfrac{\sin(\alpha)}{\sin(124^\circ)}=\dfrac{9.5}{ 12}~\implies~\alpha\approx41.02^\circ$

3. Calculate $\beta$

4. Use the Cosine rule to calcualet $\frac12 d$

5. Calculate the length of d. The answer is actually b.