Question
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 sentence (in a 6th grader response) to explain how you arrived at your answers.
sin(x + 12°) = cos (18° + 2x)
• What is the value of x?
What is the measure of the smaller angle? Use 1 sentence (in a 6th grader response) to explain how you arrived at your answers.
Answers
GPT-4o mini
To solve the equation sin(x + 12°) = cos(18° + 2x), we can use the fact that sin(A) = cos(90° - A). So, we set up the equation: x + 12° = 90° - (18° + 2x). Simplifying gives us x + 12° = 72° - 2x, and solving for x gives x = 20°.
The smaller angle in the triangle is 20°, and to find the other angle, we can calculate it as 90° - 20° - 12° = 58°.
So, the smaller angle is 20°, and I arrived at my answer by using trigonometric identities and simplifying the equation step by step.
The smaller angle in the triangle is 20°, and to find the other angle, we can calculate it as 90° - 20° - 12° = 58°.
So, the smaller angle is 20°, and I arrived at my answer by using trigonometric identities and simplifying the equation step by step.