Trig question?

ur5pointos2sl

Ok my math is a little rusty. I ran across a problem that states:
"A park is being considered in a space between a small river and a highway as a rest stop for travelers. Boundary BC is perpendicular to the highway and boundary AD makes an angle of 75 Deg. with the highway. BC= 160.0 m , AD= 270.0 m, and the boundary along the highway = 190.0m long. What are the length of side AB and the magnitude of angle ABC?"

I have attached a file that is almost identical to the one in the book. I need help figuring out where to start this problem(not an answer please). Any help would be appreciated.

Thanks

Attached Thumbnails

 

tiny-tim

Hi ur5pointos2sl ! Welcome to PF!

I can't see your picture file yet, but I think the best way is probably to use x and y coordinates, starting with C as the origin.

ur5pointos2sl

My problem is that I cant seem to use law of sine/cosine because there is always 2 things to be solved for. I think I am missing something.

I put C at the origin and looked at it that way. If i seperate the figure into two triangles that doesn't seem to lead me anywhere either. I can solve for one but then the other I am completely stuck on.

Dick

You don't need coordinates. DO split the quadrilateral into two triangles. Solve the right triangle first. Find length of BD and the two angles. Then you have side-angle-side on the remaining triangle. Solve it.

ur5pointos2sl

Thank you. That is exactly what I did last night except I solved for the right triangle then used law of cosine to solve for the other. I finally realized my answer was off because I was rounding to one decimal place.