![\bf \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{sin(75^o)}{17}=\cfrac{sin(D)}{10}\implies \cfrac{10sin(75^o)}{17}=sin(D) \\\\\\ sin^{-1}\left[ \cfrac{10sin(75^o)}{17} \right]=D\implies 34.6\approx D](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BLaw%20of%20sines%7D%20%5C%5C%5C%5C%20%5Ccfrac%7Bsin%28%5Cmeasuredangle%20A%29%7D%7Ba%7D%3D%5Ccfrac%7Bsin%28%5Cmeasuredangle%20B%29%7D%7Bb%7D%3D%5Ccfrac%7Bsin%28%5Cmeasuredangle%20C%29%7D%7Bc%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Ccfrac%7Bsin%2875%5Eo%29%7D%7B17%7D%3D%5Ccfrac%7Bsin%28D%29%7D%7B10%7D%5Cimplies%20%5Ccfrac%7B10sin%2875%5Eo%29%7D%7B17%7D%3Dsin%28D%29%20%5C%5C%5C%5C%5C%5C%20sin%5E%7B-1%7D%5Cleft%5B%20%5Ccfrac%7B10sin%2875%5Eo%29%7D%7B17%7D%20%5Cright%5D%3DD%5Cimplies%2034.6%5Capprox%20D)
since all interior angles in a triangle must be 180°, that means that C = 180 - 75 - 34.6 = 70.4. Let's find AD, which is the other sides pair length.
![\bf \cfrac{sin(75^o)}{17}=\cfrac{sin(70.4^o)}{AD}\implies ADsin(75^o)=17sin(70.4^o) \\\\\\ AD=\cfrac{17sin(70.4^o)}{sin(75^o)}\implies AD\approx 16.58](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7Bsin%2875%5Eo%29%7D%7B17%7D%3D%5Ccfrac%7Bsin%2870.4%5Eo%29%7D%7BAD%7D%5Cimplies%20ADsin%2875%5Eo%29%3D17sin%2870.4%5Eo%29%20%5C%5C%5C%5C%5C%5C%20AD%3D%5Ccfrac%7B17sin%2870.4%5Eo%29%7D%7Bsin%2875%5Eo%29%7D%5Cimplies%20AD%5Capprox%2016.58)
now, check the picture below, let's find the altitude of the parallelogram.
![\bf sin(34.6^o)=\cfrac{\stackrel{opposite}{h}}{\stackrel{hypotenuse}{16.58}}\implies 16.58sin(34.6^o)=h\implies 9.4\approx h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=9.4 \end{cases}\implies A=(17)(9.4)\implies A=159.8](https://tex.z-dn.net/?f=%5Cbf%20sin%2834.6%5Eo%29%3D%5Ccfrac%7B%5Cstackrel%7Bopposite%7D%7Bh%7D%7D%7B%5Cstackrel%7Bhypotenuse%7D%7B16.58%7D%7D%5Cimplies%2016.58sin%2834.6%5Eo%29%3Dh%5Cimplies%209.4%5Capprox%20h%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ctextit%7Barea%20of%20a%20parallelogram%7D%5C%5C%5C%5C%20A%3Dbh~~%20%5Cbegin%7Bcases%7D%20b%3Dbase%5C%5C%20h%3Dheight%5C%5C%20%5Ccline%7B1-1%7D%20b%3D17%5C%5C%20h%3D9.4%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%2817%29%289.4%29%5Cimplies%20A%3D159.8)
Answer:
8% interest rate
Step-by-step explanation:
step-by-step explanation: intrest = 484
If y=3.75x, then x/3.75 is y. The answer is 0.75 of an hour, which is 45 minutes.
True Statements
It has one face that is a decagon.
It has 11 faces.
It has 20 edges.
False Statements
It has two faces that are decagons.
It has 20 vertices.