EL VECTOR RESULTANTE DE LA SUMA DE 2 VECTORES TIENE 30 UNIDADES DE LONGITUD Y HACE ÁNGULOS DE 25º Y 50º CON ELLOS.HALLAR LA MAGNITUD DE LOS 2 VECTORES
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![Hola \\ \\ En~la~figura~abajo~elegimos~dos~vectores~\vec{a}~y~\vec{b}~cuyo~resultante~es \\ el~vector~[\vec{R}=30u],para~calcular~las~magnitudes~usarenis~la~lei~de~ \\ senos, veamos: \\ \\ \frac{\vec{a}}{sen25\°}= \frac{\vec{b}}{sen50\°}= \frac{\vec{R}}{sen105\° }~~--\ \textgreater \ ahora~igualemos~observe: \\ \\ \frac{\vec{a}}{sen25\°}= \frac{\vec{R}}{sen105\°} ~~~--\ \textgreater \ sabemos~que[\vec{R}=30u], reemplazando \\ \\ \frac{\vec{a}}{sen25\°}= \frac{30}{sen105\° } ~~--\ \textgreater \ despejemos~\vec{a} \\ \\ \\](https://tex.z-dn.net/?f=Hola++%5C%5C++%5C%5C+En%7Ela%7Efigura%7Eabajo%7Eelegimos%7Edos%7Evectores%7E%5Cvec%7Ba%7D%7Ey%7E%5Cvec%7Bb%7D%7Ecuyo%7Eresultante%7Ees+%5C%5C+el%7Evector%7E%5B%5Cvec%7BR%7D%3D30u%5D%2Cpara%7Ecalcular%7Elas%7Emagnitudes%7Eusarenis%7Ela%7Elei%7Ede%7E+%5C%5C+senos%2C+veamos%3A+%5C%5C++%5C%5C++%5Cfrac%7B%5Cvec%7Ba%7D%7D%7Bsen25%5C%C2%B0%7D%3D+%5Cfrac%7B%5Cvec%7Bb%7D%7D%7Bsen50%5C%C2%B0%7D%3D+%5Cfrac%7B%5Cvec%7BR%7D%7D%7Bsen105%5C%C2%B0+%7D%7E%7E--%5C+%5Ctextgreater+%5C+ahora%7Eigualemos%7Eobserve%3A+%5C%5C++%5C%5C++%5Cfrac%7B%5Cvec%7Ba%7D%7D%7Bsen25%5C%C2%B0%7D%3D+%5Cfrac%7B%5Cvec%7BR%7D%7D%7Bsen105%5C%C2%B0%7D+%7E%7E%7E--%5C+%5Ctextgreater+%5C+sabemos%7Eque%5B%5Cvec%7BR%7D%3D30u%5D%2C+reemplazando+%5C%5C++%5C%5C++%5Cfrac%7B%5Cvec%7Ba%7D%7D%7Bsen25%5C%C2%B0%7D%3D+%5Cfrac%7B30%7D%7Bsen105%5C%C2%B0+%7D++%7E%7E--%5C+%5Ctextgreater+%5C+despejemos%7E%5Cvec%7Ba%7D++%5C%5C++%5C%5C++%5C%5C++ "Hola \\ \\ En~la~figura~abajo~elegimos~dos~vectores~\vec{a}~y~\vec{b}~cuyo~resultante~es \\ el~vector~[\vec{R}=30u],para~calcular~las~magnitudes~usarenis~la~lei~de~ \\ senos, veamos: \\ \\ \frac{\vec{a}}{sen25\°}= \frac{\vec{b}}{sen50\°}= \frac{\vec{R}}{sen105\° }~~--\ \textgreater \ ahora~igualemos~observe: \\ \\ \frac{\vec{a}}{sen25\°}= \frac{\vec{R}}{sen105\°} ~~~--\ \textgreater \ sabemos~que[\vec{R}=30u], reemplazando \\ \\ \frac{\vec{a}}{sen25\°}= \frac{30}{sen105\° } ~~--\ \textgreater \ despejemos~\vec{a} \\ \\ \\")
![\vec{a}= \frac{30(sen25\°)}{sen105\°}~~--\ \textgreater \ valor~aproximado~de~\begin{cases}sen25\°=0,42 \\ \\ sen105\°=0,97\end{cases} \\ \\ \vec{a}= \frac{30.(0,42)}{0,97} \\ \\ \vec{a}=12,98969.....~~--\ \textgreater \ redondeando~seria \\ \\ \boxed{\boxed{\vec{a}=12,99~~o'~~ 13u} } \\ \\ ===================================== \\ Ahora~calcularemos~de~la~misma~forma~y~el~mismo~procedimiento \\ el~\vec{b}~veamos: \\ \\ \frac{\vec{b}}{sen50\°}= \frac{\vec{R}}{sen105\°} ~~--\ \textgreater \ valor~aproximado~de~[sen50\°=0,77] \\ \\](https://tex.z-dn.net/?f=%5Cvec%7Ba%7D%3D+%5Cfrac%7B30%28sen25%5C%C2%B0%29%7D%7Bsen105%5C%C2%B0%7D%7E%7E--%5C+%5Ctextgreater+%5C+valor%7Eaproximado%7Ede%7E%5Cbegin%7Bcases%7Dsen25%5C%C2%B0%3D0%2C42+%5C%5C++%5C%5C+sen105%5C%C2%B0%3D0%2C97%5Cend%7Bcases%7D+%5C%5C++%5C%5C+%5Cvec%7Ba%7D%3D+%5Cfrac%7B30.%280%2C42%29%7D%7B0%2C97%7D++%5C%5C++%5C%5C+%5Cvec%7Ba%7D%3D12%2C98969.....%7E%7E--%5C+%5Ctextgreater+%5C+redondeando%7Eseria+%5C%5C++%5C%5C+%5Cboxed%7B%5Cboxed%7B%5Cvec%7Ba%7D%3D12%2C99%7E%7Eo%27%7E%7E+13u%7D+%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+Ahora%7Ecalcularemos%7Ede%7Ela%7Emisma%7Eforma%7Ey%7Eel%7Emismo%7Eprocedimiento+%5C%5C+el%7E%5Cvec%7Bb%7D%7Eveamos%3A+%5C%5C++%5C%5C++%5Cfrac%7B%5Cvec%7Bb%7D%7D%7Bsen50%5C%C2%B0%7D%3D++%5Cfrac%7B%5Cvec%7BR%7D%7D%7Bsen105%5C%C2%B0%7D+%7E%7E--%5C+%5Ctextgreater+%5C+valor%7Eaproximado%7Ede%7E%5Bsen50%5C%C2%B0%3D0%2C77%5D+%5C%5C++%5C%5C++ "\vec{a}= \frac{30(sen25\°)}{sen105\°}~~--\ \textgreater \ valor~aproximado~de~\begin{cases}sen25\°=0,42 \\ \\ sen105\°=0,97\end{cases} \\ \\ \vec{a}= \frac{30.(0,42)}{0,97} \\ \\ \vec{a}=12,98969.....~~--\ \textgreater \ redondeando~seria \\ \\ \boxed{\boxed{\vec{a}=12,99~~o'~~ 13u} } \\ \\ ===================================== \\ Ahora~calcularemos~de~la~misma~forma~y~el~mismo~procedimiento \\ el~\vec{b}~veamos: \\ \\ \frac{\vec{b}}{sen50\°}= \frac{\vec{R}}{sen105\°} ~~--\ \textgreater \ valor~aproximado~de~[sen50\°=0,77] \\ \\")
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al0ndr4
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