Calcula la altura de un árbol, sabiendo que desde un punto del terreno se observa su copa bajo un ángulo de 30° y si nos acercamos 10 m, bajo un ángulo de 60°?

<img src="https://tex.z-dn.net/?f=Hola~~%5Cmathbb%7BFANNY%7D%20%5C%5C%20%20" /> / | / / | / / | / / | / / | h = ?

/ / | / / | / )30° / )60° | | - - 10m - - - | - - - - x - - - - - - |

<img src="https://tex.z-dn.net/?f=%5Cmathbb%7Buuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu%7D%20%20%5C%5C%20De~la~figura~primero~vamos~calcular~el%20~valor~de%28x%29~con~respecto%20%5C%5C%20al~%5Cacute%7Ba%7Dngulo~de~60%5C%C2%B0~vea%3A%20%5C%5C%20%20%5C%5C%20tg60%5C%C2%B0%3D%20%5Cfrac%7Bh%7D%7Bx%7D%20~~~--%5C%20%5Ctextgreater%20%5C%20valor~aproximado~de~%5Btg60%5C%C2%B0%3D1%2C7%5D%20%5C%5C%20%20%5C%5C%201%2C7%3D%20%5Cfrac%7Bh%7D%7Bx%7D%20~~--%5C%20%5Ctextgreater%20%5C%20despejando~%28x%29~tenemos%3A%20%5C%5C%20%20%5C%5C%20%5Cboxed%7Bx%3D%20%5Cfrac%7Bh%7D%7B1%2C7%7D%20%7D~-----%5C%20%5Ctextgreater%20%5C%20%28I%29%20%5C%5C%20%20%5C%5C%20%5Cmathbb%7Buuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu%7D%20%5C%5C%20%20%5C%5C%20Ahora~calculamos~con~respecto~al%20~%5Cacute%7Ba%7Dngulo~de~30%5C%C2%B0~vea%3A%5C%5C%20%20%5C%5C%20" />

<img src="https://tex.z-dn.net/?f=tg30%5C%C2%B0%3D%20%5Cfrac%7Bh%7D%7B10%2Bx%7D%20~~--%5C%20%5Ctextgreater%20%5C%20valor~aproximado~de~%5Btg30%5C%C2%B0%3D0%2C6%5D%20%20%5C%5C%20%20%5C%5C%200%2C6%3D%20%5Cfrac%7Bh%7D%7B10%2Bx%7D~~--%5C%20%5Ctextgreater%20%5C%20despejamos~%28h%29~tenemos%3A%20%5C%5C%20%20%5C%5C%20%5Cboxed%7Bh%3D0%2C6%2810%2Bx%29%20%7D~~-------%5C%20%5Ctextgreater%20%5C%20%28II%29%20%5C%5C%20%20%5C%5C%20%5Cmathbb%7Buuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu%7D%20%5C%5C%20Ahora~para~calcular~el~valor~de~%28h%29~reemplazamos~%28I%29~en~%28II%29~vea%3A%20%5C%5C%20%20%5C%5C%20%20h%3D0%2C6%2810%2Bx%29~~--%5C%20%5Ctextgreater%20%5C%20sabemos~que~%5Bx%3D%20%5Cfrac%7Bh%7D%7B1%2C7%7D%5D%20%5C%5C%20%20%5C%5C%20h%3D0%2C6%2810%2B%20%5Cfrac%7Bh%7D%7B1%2C7%7D%29~~--%5C%20%5Ctextgreater%20%5C%20operando~queda%3A%20%5C%5C%20%20%5C%5C%20h%3D6%2B0%2C4h%20%20%5C%5C%20%20%5C%5C%20" />

<img src="https://tex.z-dn.net/?f=h-0%2C4h%3D6%20%5C%5C%20%20%5C%5C%200%2C6h%3D6%20%5C%5C%20%20%5C%5C%20h%3D%20%5Cfrac%7B6%7D%7B0%2C6%7D%20%20%5C%5C%20%20%5C%5C%20%5Cboxed%7Bh%3D10m%7D~~--%5C%20%5Ctextgreater%20%5C%20~altura~del~arbol%20%5C%5C%20%20%5C%5C%20%5Cmathbb%7Buuuuuuuuuuuuuuuuuuuuuuuuuuuuuu%7D%20%5C%5C%20~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~te~sirva~saludos%21%21%20%5C%5C%20%20%5C%5C%20" />.