Question

Given that sin(x+10)=cos(3x+20), find the number of degrees in the acute angles of the corresponding right triangle.

Answer 1

therefore x=15
x + 10 = 15+10=25
3x+20= 3×15+20=45+20=65

Answer 2

To find the number of degrees in the acute angles of the corresponding right triangle (x):

• sin(x+10) = cos(3x+20)
• We know that, sinx = cos(90-x) and cosx = sin(90-x); sin(x+10) = sin(90-(3x+20))
• sin(x+10) = sin(90-3x-20)
• sin(x+10) = sin(70-3x)
• x + 10 = 70 -3x
• 4x = 60
• x = 15 degrees

Thus, the answer is 15 degrees acute angles of corresponding right triangle.