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In square ABCD, P is the midpoint of BC, and Q is the midpoint of CD. Find sin angle APQ.

 Apr 21, 2021
 #1
avatar+527 
+1

https://gyazo.com/eb81f42a01d41413e5c0e2142e65f840

https://gyazo.com/8eb1c4fc84d610677733f0a49f80111e

https://gyazo.com/43b4aa667b149034c2b1db4b8e91ebbe

 

Here are the pictures to my working... didn't know how to explain without pictures 

Hope this helps though :)

 

Answer ≈ 71.57o

 Apr 21, 2021
 #2
avatar+31536 
+1

See image below:

angle z   + angle apq  + 45   = 180 degree straight line

 

tan z = x / (1/2 x) = 2

arctan(2)  = z = 63.434

 

63.434 + APQ  + 45 = 180

APQ = 71.565 degrees

 

 Apr 21, 2021
 #3
avatar+1205 
+1

∠APB = arctan(2/1) = 63.43494882º

 

∠CPQ = 45º

 

∠APQ = 180 - (∠APB + ∠CPQ) = 71.56505118º

 

sin(∠APQ) = 0.948683298 laugh

 Apr 21, 2021

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