Question

A sombra de uma arvore mede 4,5m. A mesma hora, a sombra de um bastão de 0,6m, mantido na vertical, mede 0,4m. Determine a altura da arvore.

Answer 1

$\boxed{\begin{array}{l}\rm h_a\longrightarrow altura~da~\acute arvore\\\rm h_b\longrightarrow altura~do~bast\tilde ao\\\rm s_a\longrightarrow sombra~da~\acute arvore\\\rm s_b\longrightarrow sombra~do~bast\tilde ao\\\rm\dfrac{h_a}{h_b}=\dfrac{s_a}{s_b}\\\\\rm\dfrac{h_a}{0,4}=\dfrac{4,5}{0,6}\\\\\rm 0,6h_a=0,4\cdot4,5\\\rm 0,6h_a=1,8\\\\\rm h_a=\dfrac{1,8}{0,6}\\\\\rm h_a=3~m\end{array}}$