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 √3/2 3 1/2

Explanation:

Step1: Recall the Pythagorean Theorem

For a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. In a unit circle, the hypotenuse \(c = 1\) (radius of the unit circle), and let \(a=\frac{1}{2}\), we need to find \(b\).

Step2: Substitute values into the formula

Substitute \(a=\frac{1}{2}\) and \(c = 1\) into \(a^{2}+b^{2}=c^{2}\). We get \((\frac{1}{2})^{2}+b^{2}=1^{2}\).

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Step3: Solve for \(b\)

Take the square root of both sides. Since \(b>0\) (length of a side of a triangle), \(b=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\)

Answer:

\(\frac{\sqrt{3}}{2}\)