Calcular la altura de una arbol sabiendo que desde un punto del terreno se observa su copa bajo un angulo de 30grados y si nos acercamos 10m bajo un angulo de 60grados
Respuestas
Respuesta:
/|
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/ / |
/ / |
/ / | h=?
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/ )30° /)60° |
|--10m---|----x------|
\begin{gathered}\mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ De~la~figura~primero~vamos~calcular~el ~valor~de(x)~con~respecto \\ al~\acute{a}ngulo~de~60\°~vea: \\ \\ tg60\°= \frac{h}{x} ~~~--\ \textgreater \ valor~aproximado~de~[tg60\°=1,7] \\ \\ 1,7= \frac{h}{x} ~~--\ \textgreater \ despejando~(x)~tenemos: \\ \\ \boxed{x= \frac{h}{1,7} }~-----\ \textgreater \ (I) \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ \\ Ahora~calculamos~con~respecto~al ~\acute{a}ngulo~de~30\°~vea:\\ \\ \end{gathered}
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De la figura primero vamos calcular el valor de(x) con respecto
al
a
ˊ
ngulo de 60\° vea:
tg60\°=
x
h
−− \textgreater valor aproximado de [tg60\°=1,7]
1,7=
x
h
−− \textgreater despejando (x) tenemos:
x=
1,7
h
−−−−− \textgreater (I)
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Ahora calculamos con respecto al
a
ˊ
ngulo de 30\° vea:
\begin{gathered}tg30\°= \frac{h}{10+x} ~~--\ \textgreater \ valor~aproximado~de~[tg30\°=0,6] \\ \\ 0,6= \frac{h}{10+x}~~--\ \textgreater \ despejamos~(h)~tenemos: \\ \\ \boxed{h=0,6(10+x) }~~-------\ \textgreater \ (II) \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ Ahora~para~calcular~el~valor~de~(h)~reemplazamos~(I)~en~(II)~vea: \\ \\ h=0,6(10+x)~~--\ \textgreater \ sabemos~que~[x= \frac{h}{1,7}] \\ \\ h=0,6(10+ \frac{h}{1,7})~~--\ \textgreater \ operando~queda: \\ \\ h=6+0,4h \\ \\ \end{gathered}
tg30\°=
10+x
h
−− \textgreater valor aproximado de [tg30\°=0,6]
0,6=
10+x
h
−− \textgreater despejamos (h) tenemos:
h=0,6(10+x)
−−−−−−− \textgreater (II)
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Ahora para calcular el valor de (h) reemplazamos (I) en (II) vea:
h=0,6(10+x) −− \textgreater sabemos que [x=
1,7
h
]
h=0,6(10+
1,7
h
) −− \textgreater operando queda:
h=6+0,4h
\begin{gathered}h-0,4h=6 \\ \\ 0,6h=6 \\ \\ h= \frac{6}{0,6} \\ \\ \boxed{h=10m}~~--\ \textgreater \ ~altura~del~arbol \\ \\ \mathbb{uuuuuuuuuuuuuuuuuuuuuuuuuuuuuu} \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~te~sirva~saludos!! \\ \\ \end{gathered}
h−0,4h=6
0,6h=6
h=
0,6
6
h=10m
−− \textgreater altura del arbol
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Espero te sirva saludos!!