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.

Answer 1

To find the value of x, we can use the relationship between sin and cos functions. We can set sin(x + 12°) equal to cos(90° - (x + 12°)), and then set those expressions equal to cos(18° + 2x). By equating those expressions, we can solve for x, which will give us the measure of the smaller angle.

Answer 2

so whats the answer?

Answer 3

The value of x is 27°, and the measure of the smaller angle is 39°. This is obtained by equating sin(x + 12°) to cos(90° - (x + 12°)), and setting that expression equal to cos(18° + 2x), which can be solved for x.