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?

queendaddy
Apr 25, 2018

#1**+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

CPhill
Apr 25, 2018