# A parallelogram has a side length of 3 and the other side is 5. One angle equals 50 degrees. What are the lengths of the diagonals?

Nov 8, 2016

Lengths of diagonals (approx.): $7.3 \mathmr{and} 3.8$

#### Explanation:

Based on the image below:

$h = 3 \sin \left({50}^{\circ}\right) \approx 2.298133329$

$x = 3 \cos \left({50}^{\circ}\right) \approx 1.928362829$

Long diagonal
$\textcolor{w h i t e}{\text{XXX}} {d}_{L} = \sqrt{{h}^{2} + {\left(5 + x\right)}^{2}} \approx 7.299563569$

Short diagonal
$\textcolor{w h i t e}{\text{XXX}} {d}_{S} = \sqrt{{h}^{2} + {\left(5 - x\right)}^{2}} \approx 3.836192345$