X^2 = 12^2 + 10^2
x^2 = 144 + 100
x^2 = 244
x = sqrt(244)
x = 15.62
First off, let's notice that the angle is in the IV Quadrant, where sine is negative and the cosine is positive, likewise the opposite and adjacent angles respectively.
Also let's bear in mind that the hypotenuse is never negative, since it's simply just a radius unit.
![\bf cot(\theta )=\cfrac{\stackrel{adjacent}{6}}{\stackrel{opposite}{-7}}\qquad \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{6^2+(-7)^2}\implies c=\sqrt{36+49}\implies c=\sqrt{85} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20cot%28%5Ctheta%20%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B6%7D%7D%7B%5Cstackrel%7Bopposite%7D%7B-7%7D%7D%5Cqquad%20%5Cimpliedby%20%5Ctextit%7Blet%27s%20find%20the%20%5Cunderline%7Bhypotenuse%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Ctextit%7Busing%20the%20pythagorean%20theorem%7D%20%5C%5C%5C%5C%20c%5E2%3Da%5E2%2Bb%5E2%5Cimplies%20c%3D%5Csqrt%7Ba%5E2%2Bb%5E2%7D%20%5Cqquad%20%5Cbegin%7Bcases%7D%20c%3Dhypotenuse%5C%5C%20a%3Dadjacent%5C%5C%20b%3Dopposite%5C%5C%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20c%3D%5Csqrt%7B6%5E2%2B%28-7%29%5E2%7D%5Cimplies%20c%3D%5Csqrt%7B36%2B49%7D%5Cimplies%20c%3D%5Csqrt%7B85%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf tan(\theta)=\cfrac{\stackrel{opposite}{-7}}{\stackrel{adjacent}{6}} ~\hfill csc(\theta)=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{opposite}{-7}} ~\hfill sec(\theta)=\cfrac{\stackrel{hypotenuse}{\sqrt{85}}}{\stackrel{adjacent}{6}} \\\\\\ sin(\theta)=\cfrac{\stackrel{opposite}{-7}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{sin(\theta)=\cfrac{-7}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies sin(\theta)=-\cfrac{7\sqrt{85}}{85}}](https://tex.z-dn.net/?f=%5Cbf%20tan%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B-7%7D%7D%7B%5Cstackrel%7Badjacent%7D%7B6%7D%7D%20~%5Chfill%20csc%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Bhypotenuse%7D%7B%5Csqrt%7B85%7D%7D%7D%7B%5Cstackrel%7Bopposite%7D%7B-7%7D%7D%20~%5Chfill%20sec%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Bhypotenuse%7D%7B%5Csqrt%7B85%7D%7D%7D%7B%5Cstackrel%7Badjacent%7D%7B6%7D%7D%20%5C%5C%5C%5C%5C%5C%20sin%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7B-7%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B%5Csqrt%7B85%7D%7D%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Band%20rationalizing%20the%20denominator%7D%7D%7Bsin%28%5Ctheta%29%3D%5Ccfrac%7B-7%7D%7B%5Csqrt%7B85%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%7B85%7D%7D%7B%5Csqrt%7B85%7D%7D%5Cimplies%20sin%28%5Ctheta%29%3D-%5Ccfrac%7B7%5Csqrt%7B85%7D%7D%7B85%7D%7D)
![\bf cos(\theta)=\cfrac{\stackrel{adjacent}{6}}{\stackrel{hypotenuse}{\sqrt{85}}}\implies \stackrel{\textit{and rationalizing the denominator}}{cos(\theta)=\cfrac{6}{\sqrt{85}}\cdot \cfrac{\sqrt{85}}{\sqrt{85}}\implies cos(\theta)=\cfrac{6\sqrt{85}}{85}}](https://tex.z-dn.net/?f=%5Cbf%20cos%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7Badjacent%7D%7B6%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B%5Csqrt%7B85%7D%7D%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Band%20rationalizing%20the%20denominator%7D%7D%7Bcos%28%5Ctheta%29%3D%5Ccfrac%7B6%7D%7B%5Csqrt%7B85%7D%7D%5Ccdot%20%5Ccfrac%7B%5Csqrt%7B85%7D%7D%7B%5Csqrt%7B85%7D%7D%5Cimplies%20cos%28%5Ctheta%29%3D%5Ccfrac%7B6%5Csqrt%7B85%7D%7D%7B85%7D%7D)
Answer:
9(1 +6)
Step-by-step explanation:
9 = 9 * 1
54 = 9 * 6
9 + 54 = (9*1 ) + (9*6) {9 is common in both terms}
= 9*(1 + 6)
72 × 1.4666666666667 = 105.6 feet per second
Answer:
this is my 50th time seeing you
Step-by-step explanation: