Question

Caminhando num parque. Maria vê o topo de obelisco sob angulo de 30 . Aproximando-se n 20 metros passa a vê-lo sob o angulo 60. qual e a altura do obelisco

Answer 1

$\textrm{Calculando \textbf{x} pela lei dos senos:}\\\\ \mathrm{\dfrac{x}{\sin{120\º}}=\dfrac{20}{\sin{30\º}}\ \to\ \dfrac{x}{\frac{\sqrt{3}}{2}}=\dfrac{20}{\frac{1}{2}}}\\\\ \mathrm{\dfrac{x}{2}=\dfrac{20\sqrt{3}}{2}\ \to\ x=20\sqrt{3}\ m}\\\\ \textrm{Calculando \textbf{h}:}\\\\ \mathrm{\sin{30\º}=\dfrac{h}{x}\ \to\ h=x.\sin{30\º}}\\\\ \mathrm{h=20\sqrt{3}.\dfrac{1}{2}\ \to\ \mathbf{h=10\sqrt{3}\ m}}$