# Find the solution sin Y = cos ( Y + 20° )

Question
Find the solution $$\displaystyle{\sin{{Y}}}={\cos{{\left({Y}+{20}°\right)}}}$$

2021-03-08
In a right triangle the two acute angles add up to 90°. This means that the cosine of one angle is the sine of the other. So Y+Y+20=90, 2Y=70, Y=35°. There are other solutions but both the angles will not be acute.

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$$\displaystyle{\sin{{\left({x}°-{20}°\right)}}}={\cos{{42}}}°$$ for x, where 0 < x < 90