In a right triangle, the acute angles have the relationship sin(x+12°)=cos(18°+2x)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)
To solve for x, we can take the sine of both sides of the equation to get sin(x+12°)=sin(72°-2x). From there, we can set the angles inside the sine functions equal to each other, giving us x+12°=72°-2x. Simplifying this equation, we find that 3x=60°, so x=20°. Since the acute angles in a right triangle add up to 90°, the measure of the smaller angle is 20°.
