Question

Determine o valor da altura AD do triângulo ABC.

Answer 1

$\boxed{\begin{array}{l}\sf BC^2=AB^2+AC^2\\\sf BC^2=6^2+10^2\\\sf BC^2=36+100\\\sf BC^2=136\\\sf BC=\sqrt{136}\\\sf BC=2\sqrt{34}\\\sf BC\cdot AD=AB\cdot AC\\\sf AD=\dfrac{AB\cdot AC}{BC}\\\\\sf AD=\dfrac{\diagup\!\!\!6^3\cdot10}{\diagup\!\!\!2\sqrt{34}}=\dfrac{30}{\sqrt{34}}\end{array}}$

$\boxed{\begin{array}{l}\sf AD=\dfrac{\diagdown\!\!\!\!\!\!30^{15}\sqrt{34}}{\diagdown\!\!\!\!\!\!34_{17}}\\\\\sf h=\dfrac{15\sqrt{34}}{17}\end{array}}$