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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

 Jun 23, 2023
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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)  =  38.66o    

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

                                                    total      49.97o   

 

Angle PAQ  =  90o minus 49.97o  =  40.03o     

 

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. 

.

 Jul 14, 2023

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