+68 In square ABCD, P is on BC such that BP=4 and PC=1, and Q is on CD such that DQ=4 and QC=1. Find sin of angle PAQ.
+1557 To find the sine of angle PAQ, we need to find the length of PQ and the length of AP.
To find the length of PQ, we can use the Pythagorean Theorem on triangle BPQ.
PQ2=BP2+PC2=42+12=17
PQ=17
To find the length of AP, we can use the Pythagorean Theorem on triangle APQ.
AP2=AQ2+PQ2=52+17=42
AP=42=67
Now that we know the length of PQ and AP, we can find the sine of angle PAQ using the definition of sine:
sin(PAQ) = opposite/hypotenuse = PQ/AP = sqrt(17)/(6*sqrt(7)) = sqrt(119)/42.
