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

Guest Jun 23, 2023

#1**0 **

*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.

_{.}

Bosco Jul 14, 2023