quadrilateral missing sides

[clarkymk]

Hi. I've been doing a bit of trigonometry recently. I like to just draw random things and see if I can find various angles, sides and areas. I came up with this one this morning and I'm not sure what to do with it.

Please can someone help me figure it out?

I put illustrated it in Serif Drawplus to make it look nice for you.

Thanks.
-matt

 

[stapel]

Hi. I've been doing a bit of trigonometry recently. I like to just draw random things and see if I can find various angles, sides and areas. I came up with this one this morning and I'm not sure what to do with it.

Please reply with a clear listing of your thoughts and efforts so far. When you reply, please include a listing of recent topics of study, as this may influence the helps and hints that the volunteers provide. Thank you!

 

[clarkymk]

A possible solution

The sections in green were that parts I worked on. Today I tried to draw it proportionally on a grid and I had a bit of a break through. I cut the awkward shape down into two simple triangles and a rectangle - then used Pythagoras to work out the missing sides. I my findings are correct:

Line a = 4.03 (to 2 decimal places)

Line b = 6.18 (to 2 decimal places)

Although...
I'm wondering if there might be way to work it out that doesn't require a computer program with precise shape transformations. I would love to find an algebraic method that can be used quickly on paper to solve any example.
I hope to hear your suggestions.

Thank you

have a nice day

-matt