Question

Qual a área do triângulo retângulo ABC da figura, sabendo que o segmento BC é igual a 20 m e cos =4 5⁄?

Answer 1

Resposta:

A = 96 m²

Explicação passo a passo:

$cos\alpha=\frac{4}{5} \\\\BC=20m\\\\cos\alpha =\frac{AC}{BC}\\\\\frac{4}{5}=\frac{AC}{20} \\\\5AC=4.20\\\\AC=4.4\\\\AC=16m\\\\(AC)^2+16^2=20^2\\\\(AC)^2+256=400\\\\(AC)^2=400-256\\\\(AC)^2=144\\\\AC=12m\\\\A=\frac{AC.AB}{2} \\\\A=\frac{16.12}{2}\\\\A=8.12\\\\A=96~ m^2$