¿como se resuelve este problema de matematicas?
muchas gracias
muchas gracias
yexs
![Hola \\ \\ De~la~figura~resolvemos~com~respecto~al~\acute{a}ngulo~de~30\° asi': \\ \\ cos30\°= \frac{SR}{SQ} ~~~---\ \textgreater \ valor~aproximado~de~[cos30\°=0,87~] \\ \\ \underbrace{cos30\°}_{0,87}= \frac{SR}{SQ}~~--\ \textgreater \ y~valor~de~[SQ=250m], reemplazando \\ \\ 0,87= \frac{SR}{250} ~~---\ \textgreater \ despejamos~(SR), nos~queda \\ \\ \boxed{SR=217,5m} \\ \\ ===================================== \\ Continuamos ~com~respecto~al~\acute{a}ngulo~de~30\°, de ~la~figura~calculemos \\ ''QR'', veamos:\\ \\](https://tex.z-dn.net/?f=Hola++%5C%5C++%5C%5C+De%7Ela%7Efigura%7Eresolvemos%7Ecom%7Erespecto%7Eal%7E%5Cacute%7Ba%7Dngulo%7Ede%7E30%5C%C2%B0+asi%27%3A+%5C%5C++%5C%5C+cos30%5C%C2%B0%3D+%5Cfrac%7BSR%7D%7BSQ%7D+%7E%7E%7E---%5C+%5Ctextgreater+%5C+valor%7Eaproximado%7Ede%7E%5Bcos30%5C%C2%B0%3D0%2C87%7E%5D+%5C%5C++%5C%5C+%5Cunderbrace%7Bcos30%5C%C2%B0%7D_%7B0%2C87%7D%3D+%5Cfrac%7BSR%7D%7BSQ%7D%7E%7E--%5C+%5Ctextgreater+%5C+y%7Evalor%7Ede%7E%5BSQ%3D250m%5D%2C+reemplazando+%5C%5C++%5C%5C+0%2C87%3D+%5Cfrac%7BSR%7D%7B250%7D++%7E%7E---%5C+%5Ctextgreater+%5C+despejamos%7E%28SR%29%2C+nos%7Equeda+%5C%5C++%5C%5C+%5Cboxed%7BSR%3D217%2C5m%7D+%5C%5C++%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C+Continuamos+%7Ecom%7Erespecto%7Eal%7E%5Cacute%7Ba%7Dngulo%7Ede%7E30%5C%C2%B0%2C+de+%7Ela%7Efigura%7Ecalculemos+%5C%5C+%27%27QR%27%27%2C+veamos%3A%5C%5C++%5C%5C++ "Hola \\ \\ De~la~figura~resolvemos~com~respecto~al~\acute{a}ngulo~de~30\° asi': \\ \\ cos30\°= \frac{SR}{SQ} ~~~---\ \textgreater \ valor~aproximado~de~[cos30\°=0,87~] \\ \\ \underbrace{cos30\°}_{0,87}= \frac{SR}{SQ}~~--\ \textgreater \ y~valor~de~[SQ=250m], reemplazando \\ \\ 0,87= \frac{SR}{250} ~~---\ \textgreater \ despejamos~(SR), nos~queda \\ \\ \boxed{SR=217,5m} \\ \\ ===================================== \\ Continuamos ~com~respecto~al~\acute{a}ngulo~de~30\°, de ~la~figura~calculemos \\ ''QR'', veamos:\\ \\")
![sen30\°= \frac{QR}{SQ}~~--\ \textgreater \ valor~de~[sen30\°=0,5]~y~[SQ=250~] \\ \\ 0,5= \frac{QR}{250} ~~---\ \textgreater \ despejemos~''QR'' \\ \\ \boxed{ QR=125m } \\ \\ =================================== \\ Ahora~calculemos~com~respecto~al~\acute{a}ngulo~total ~de~''S''~que~es~ \\ 30\°+10\°=40\° \\ De~la~figura~para~calcular~''PQ'', calcularemos~com~respecto \\ al~\acute{a}ngulo~de~40\°, veamos: \\ \\ tg40\°= \frac{PR}{SR} ~~--\ \textgreater \ valor~aproximado~de~[tg40\°=0,84~]\\ \\](https://tex.z-dn.net/?f=sen30%5C%C2%B0%3D+%5Cfrac%7BQR%7D%7BSQ%7D%7E%7E--%5C+%5Ctextgreater+%5C+valor%7Ede%7E%5Bsen30%5C%C2%B0%3D0%2C5%5D%7Ey%7E%5BSQ%3D250%7E%5D+%5C%5C++%5C%5C+0%2C5%3D+%5Cfrac%7BQR%7D%7B250%7D+%7E%7E---%5C+%5Ctextgreater+%5C+despejemos%7E%27%27QR%27%27+%5C%5C++%5C%5C+%5Cboxed%7B+QR%3D125m+%7D+%5C%5C++%5C%5C+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D+%5C%5C+Ahora%7Ecalculemos%7Ecom%7Erespecto%7Eal%7E%5Cacute%7Ba%7Dngulo%7Etotal+%7Ede%7E%27%27S%27%27%7Eque%7Ees%7E+%5C%5C+30%5C%C2%B0%2B10%5C%C2%B0%3D40%5C%C2%B0+%5C%5C+De%7Ela%7Efigura%7Epara%7Ecalcular%7E%27%27PQ%27%27%2C+calcularemos%7Ecom%7Erespecto+%5C%5C+al%7E%5Cacute%7Ba%7Dngulo%7Ede%7E40%5C%C2%B0%2C+veamos%3A+%5C%5C++%5C%5C+tg40%5C%C2%B0%3D+%5Cfrac%7BPR%7D%7BSR%7D+%7E%7E--%5C+%5Ctextgreater+%5C+valor%7Eaproximado%7Ede%7E%5Btg40%5C%C2%B0%3D0%2C84%7E%5D%5C%5C++%5C%5C++ "sen30\°= \frac{QR}{SQ}~~--\ \textgreater \ valor~de~[sen30\°=0,5]~y~[SQ=250~] \\ \\ 0,5= \frac{QR}{250} ~~---\ \textgreater \ despejemos~''QR'' \\ \\ \boxed{ QR=125m } \\ \\ =================================== \\ Ahora~calculemos~com~respecto~al~\acute{a}ngulo~total ~de~''S''~que~es~ \\ 30\°+10\°=40\° \\ De~la~figura~para~calcular~''PQ'', calcularemos~com~respecto \\ al~\acute{a}ngulo~de~40\°, veamos: \\ \\ tg40\°= \frac{PR}{SR} ~~--\ \textgreater \ valor~aproximado~de~[tg40\°=0,84~]\\ \\")
![0,84= \frac{PR}{SR} ~~--\ \textgreater \ Se~sabe~que~[PR=PQ+QR]~y~[SR=217,5] \\ \\ 0,84= \frac{PQ+QR}{217,5} \\ \\ 0,84(217,5)=PQ+QR~~--\ \textgreater \ se~sabe~tambien~que~[QR=125] \\ \\ 182,7=PQ+125~~--\ \textgreater \ despejado~''PQ'', tenemos \\ \\ PQ=182,7-125 \\ \\ \boxed{\boxed{PQ=57,7m} } \\ \\](https://tex.z-dn.net/?f=0%2C84%3D+%5Cfrac%7BPR%7D%7BSR%7D+%7E%7E--%5C+%5Ctextgreater+%5C+Se%7Esabe%7Eque%7E%5BPR%3DPQ%2BQR%5D%7Ey%7E%5BSR%3D217%2C5%5D+%5C%5C++%5C%5C+0%2C84%3D+%5Cfrac%7BPQ%2BQR%7D%7B217%2C5%7D+%5C%5C++%5C%5C+0%2C84%28217%2C5%29%3DPQ%2BQR%7E%7E--%5C+%5Ctextgreater+%5C+se%7Esabe%7Etambien%7Eque%7E%5BQR%3D125%5D+%5C%5C++%5C%5C+182%2C7%3DPQ%2B125%7E%7E--%5C+%5Ctextgreater+%5C+despejado%7E%27%27PQ%27%27%2C+tenemos+%5C%5C++%5C%5C+PQ%3D182%2C7-125+%5C%5C++%5C%5C+%5Cboxed%7B%5Cboxed%7BPQ%3D57%2C7m%7D+%7D+%5C%5C++%5C%5C++ "0,84= \frac{PR}{SR} ~~--\ \textgreater \ Se~sabe~que~[PR=PQ+QR]~y~[SR=217,5] \\ \\ 0,84= \frac{PQ+QR}{217,5} \\ \\ 0,84(217,5)=PQ+QR~~--\ \textgreater \ se~sabe~tambien~que~[QR=125] \\ \\ 182,7=PQ+125~~--\ \textgreater \ despejado~''PQ'', tenemos \\ \\ PQ=182,7-125 \\ \\ \boxed{\boxed{PQ=57,7m} } \\ \\")
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