We suppose the problem intends you to find α and β in degrees such that
.. sin(α) = cos(β) . . . . . . 0 < α < β < 90°
and
.. α = x^2 +20x
.. β = 15x^2 +2x
Then
.. (x^2 +20x) + (15x^2 +2x) = 90
.. 16x^2 +22x -90 = 0
Using the quadratic formula,
.. x = (-22 ±√(22^2 +64*90))/32 ≈ {-3.1568, +1.7818}
The positive value corresponds to
.. β ≈ 51.188°
