SOLUTION: Angles x and y are both acute angles where angle x is greater than y and the sin (x degrees)= cos(y degrees). If x=3k-11 and y=2k-9, what's the value of k? A)12 B)22 C)23.5 D)

Algebra ->  Finance -> SOLUTION: Angles x and y are both acute angles where angle x is greater than y and the sin (x degrees)= cos(y degrees). If x=3k-11 and y=2k-9, what's the value of k? A)12 B)22 C)23.5 D)      Log On


   

Question 1089351: Angles x and y are both acute angles where angle x is greater than y and the sin (x degrees)= cos(y degrees). If x=3k-11 and y=2k-9, what's the value of k?
A)12
B)22
C)23.5
D)27.5
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
It follows from the condition, that x and y are complementary angles: 

    x + y = 90 degrees.

Substitute x = 3k-11 and y = 2k-9,  and you will get an equation for k:

    (3k - 11) + (2k - 9) = 90,

5k = 90 + 11 + 9  ====>  5k = 110  ====>  k = 110%2F5 = 22 degrees.