Question

In a right triangle, the acute angles have the relationship sin(x + 12º) = cos cos(18" + 2x). What is the value of x? What is the measure of the smaller angle? Use 2 sentences to explain how you arrived at your answers. In a 6 graders response (2 points)

Answer 1

To solve for \( x \) in the right triangle, we can use the identity that \( \sin(A) = \cos(90° - A) \). This means that \( x + 12° = 90° - (18° + 2x) \), which simplifies to \( 3x = 60° \), giving \( x = 20° \); the smaller angle, which is \( x \), is \( 20° \).