Angles ∝ and β are the two acute angles in a right triangle. use the relationship between sine and cosine to find the value of β if β > ∝. sin( x 2 + 20x) = cos(2x + 15x 2 )

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°

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