Question

A right triangle has vertices at the origin, on the unit circle, and on the x-axis inside the unit circle. What is the hypotenuse of the triangle?(1 point)
Responses

0
0

3√2
the fraction with numerator square root of 3 and denominator 2

1
1

2√2

Answer 1

1

Reason: Let the x-axis point be (a,0) with |a|<1. For a right angle at (a,0) the point on the unit circle must have x=a, so it is (a, ±√(1−a^2)). The distance from the origin to that point is √(a^2 + (1−a^2)) = 1.