C) Adjacent angles whose exterior sides are perpendicular rays are complementary.
Complementary = add up to 90
Supplementary = add up to 180
![\bf tan(\theta )=\cfrac{\stackrel{opposite}{3}}{\stackrel{adjacent}{4}}\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{3^2+4^2}\implies c=5 \\\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\stackrel{hypotenuse}{5}}](https://tex.z-dn.net/?f=%5Cbf%20tan%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B3%7D%7D%7B%5Cstackrel%7Badjacent%7D%7B4%7D%7D%5Cimpliedby%20%5Ctextit%7Blet%27s%20find%20the%20%5Cunderline%7Bhypotenuse%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%5C%5C%5C%5C%0Ac%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%0A%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Ac%3Dhypotenuse%5C%5C%0Aa%3Dadjacent%5C%5C%0Ab%3Dopposite%5C%5C%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0Ac%3D%5Csqrt%7B3%5E2%2B4%5E2%7D%5Cimplies%20c%3D5%0A%5C%5C%5C%5C%5C%5C%0Asin%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B3%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B5%7D%7D)
bear in mind that, though the square has two valid roots, one negative and one positive, the hypotenuse is just a radius distance, and therefore is never negative.
Answer:
Bad
Step-by-step explanation:
Thanks
Answer:
So the expression in simplified radical form will be ![\frac{5\sqrt{3}+6}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B3%7D%2B6%7D%7B13%7D)
Step-by-step explanation:
We have have given the expression ![\frac{\sqrt{3}}{5-2\sqrt{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B5-2%5Csqrt%7B3%7D%7D)
We have to write this expression in simplest radical form
For writing in simplest radical form we have to rationalize first
So after rationalizing
![\frac{\sqrt{3}}{5-2\sqrt{3}}\times \frac{5+2\sqrt{3}}{5+2\sqrt{3}}=\frac{5\sqrt{3}+6}{25-12}=\frac{5\sqrt{3}+6}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B5-2%5Csqrt%7B3%7D%7D%5Ctimes%20%5Cfrac%7B5%2B2%5Csqrt%7B3%7D%7D%7B5%2B2%5Csqrt%7B3%7D%7D%3D%5Cfrac%7B5%5Csqrt%7B3%7D%2B6%7D%7B25-12%7D%3D%5Cfrac%7B5%5Csqrt%7B3%7D%2B6%7D%7B13%7D)
So the expression in simplified radical form will be ![\frac{5\sqrt{3}+6}{13}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B3%7D%2B6%7D%7B13%7D)