SOLUTION: If sin 6A = cos 9A, then the measure of angle A is equal to 1) 6 2) 54 3) 36 4) 1(1/2)

Algebra ->  Trigonometry-basics -> SOLUTION: If sin 6A = cos 9A, then the measure of angle A is equal to 1) 6 2) 54 3) 36 4) 1(1/2)      Log On


   

Question 951602: If sin 6A = cos 9A, then the measure of angle A is equal to
1) 6
2) 54
3) 36
4) 1(1/2)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if one of the angles of the acute angles of a right triangle is equal to 6a and the other acute angle of the triangle is equal to 9a, then the sum of both acute angles must be equal to 90 degrees.
you get:
6a + 9a = 90
solve for a to get a = 6
6a = 36
9a = 54
sin(36) = .5877852523
cos(54) = .5877852523
they're the same.
this stands to reason because:
if 6a + 9a = 90, then 9a = 90 - 6a.
by the properties of a right triangle:
sin(6a) = cos(90 - 6a)
since 90 - 6a = 9a, this means that sin(6a) = cos(9a).