Question

Angles ∝ and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of ∝ if ∝ < β.

Answer 1

Well, since we know that sin(x) = cos(90-x), we can transform the given into
2x - 8/3 = 90 - (4x - 10/3)
2x - 8/3 = 90 - 4x + 10/3
Now clear fractions by multiplying by three...

6x - 8 = 270 - 12x + 10
6x - 8 = 280 - 12x
18x = 288
x = 16
4x - 10/3 = 4(16) - 10/3 = 64 - 3.33 = 60.67 degrees.
Choice C.