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.
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.
so whats the answer?
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.
