To solve \( \sin(x + 12°) = \cos(18° + 2x) \), we can use the identity \( \cos(A) = \sin(90° - A) \) to rewrite it as \( \sin(x + 12°) = \sin(72° - 2x) \). Setting the angles equal gives us two equations, one of which leads us to find \( x = 24° \), making the smaller angle \( x = 24° \) because \( 24° < (90° - x) \).
In a right triangle, the acute angles have the relationship sin(x+12°)=cos(18°+2x)
. What is the value of x? What is the measure of the smaller angle? Use 1–2 sentences to explain how you arrived at your answers.(2 points)
Make it 2-3 sentences and make it simple.
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