Question
What is the x-coordinate of the point where the 45-45-90 triangle in this image intersects the unit circle?
Answers
GPT 3.5
In a 45-45-90 triangle, the two legs are congruent, which means each leg has a length of 1. Since the unit circle has a radius of 1, the two legs of the triangle are actually radii of the unit circle.
The 45-45-90 triangle intersects the unit circle at the points where the two congruent legs touch the circle. These points form a line called the diagonal of the square inscribed in the circle.
Since each leg of the triangle is a radius of the circle, the diagonal intersects the circle at points that are 1 radius away from the origin along the x and y-axis.
The coordinate on the x-axis where the diagonal intersects the unit circle is (1, 0).
Therefore, the x-coordinate of the point where the 45-45-90 triangle intersects the unit circle is 1.
The 45-45-90 triangle intersects the unit circle at the points where the two congruent legs touch the circle. These points form a line called the diagonal of the square inscribed in the circle.
Since each leg of the triangle is a radius of the circle, the diagonal intersects the circle at points that are 1 radius away from the origin along the x and y-axis.
The coordinate on the x-axis where the diagonal intersects the unit circle is (1, 0).
Therefore, the x-coordinate of the point where the 45-45-90 triangle intersects the unit circle is 1.