need help quick

 

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on CD such that DQ = 1 and QC = 4. Find sin angle PAQ   

 

I wish I could post a picture on here, but I can't.   

You draw the picture, and I'll provide the words.    

 

After drawing lines AP and AQ, you'll see that    

you've divided the square into three sections.   

 

Two of the sections are right triangles.  You can     

use arctan to determine angles BAP and DAQ.     

 

Add them together and subtract the total from 90.    

 

That gives you the size of angle PAQ.      

 

BAP  =   tan^–1 (4/5)  =  tan^–1 (0.8000)  =  38.66^o    

DAQ  =  tan^–1 (1/5)  =  tan^–1 (0.2000)  =  11.31^o     

                                                    total      49.97^o   

 

Angle PAQ  =  90^o minus 49.97^o  =  40.03^o     

 

I did some rounding on those arctan values, so   

my final answer might not agree exactly with the    

answer in the back of your math textbook.  Allow     

me just a wee bit of wiggle room on that, please. 

_.