Question

on the unit circle, a right triangle with an angle measure of θ has a leg opposite of θ with a length of 1/2 what is the length of the other leg? use the pythagorean theorem. (1 point) 2 1/2 3 √3/2

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle on the unit circle, if the hypotenuse $c = 1$ (radius of unit circle), and one leg $a=\frac{1}{2}$, and the other leg is $b$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$.

Step2: Substitute values into the formula

Substitute $a = \frac{1}{2}$ and $c = 1$ into $a^{2}+b^{2}=c^{2}$. We get $(\frac{1}{2})^{2}+b^{2}=1^{2}$, which simplifies to $\frac{1}{4}+b^{2}=1$.

Step3: Solve for $b$

Subtract $\frac{1}{4}$ from both sides: $b^{2}=1-\frac{1}{4}=\frac{3}{4}$. Then take the square root of both sides. Since $b$ represents the length of a side of a triangle, we take the positive square - root, so $b=\frac{\sqrt{3}}{2}$.

Answer:

D. $\frac{\sqrt{3}}{2}$