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1. What is the value of x?

sin(x+21)°=cos(2x+21)°

Enter your answer in the box.


2. What is the value of y?

 Apr 25, 2018
 #1
avatar+98005 
+1

sin (x + 21)  = cos (2x + 21)

 

Since these are cofunctions....the angles add to 90°

 

So  we have

 

x + 21  + 2x + 21  = 90     simplify

 

3x + 42  =  90      subtract 42 from both sides

 

3x  =  48    divide both sides by 3

 

x = 16

 

 

 

Second one

 

The triangle on the left is a 45-45-90 right triangle....the hypotenuse = 2√2

And the other two sides are 1/√2  times the hypotenuse

 

So the   common side of both triangles  =  2√2 ( 1/√2) =  2

 

Since  the triangle on the right is a 30-60-90 right triangle, the side opposite the 60° angle, y, is √3  that of the side opposite the 30° angle......and the side opposite the 30° angle  = 2

 

So...y  = √3 * 2   =     2√3

 

 

cool cool cool

 Apr 25, 2018
edited by CPhill  Apr 25, 2018

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