o proprietario de um terreno retangular medindo 10 por 31,5 m deseja instalar lampadas nos pontos C e D, conforme ilustrado na figura: Cada lampada ilumina uma regiao circular de 5 m de raio. Os segmentos AC e BD medem 2,5m. O valor em m2 mais aproximado da area do terreno iluminadas pelas lampadas e (Aproxime 3 para 1,7 e = para 3.)
Soluções para a tarefa
Resposta:61
Explicação passo-a-passo:
AB² = 5² – 2,5²
AB = 5√3/2
Logo, a área do triângulo ABC é igual a:
5√3/2 x 5/2/2 = 25√3/8
Repare, agora, que cosα = (5/2)/5 = ½
α = 60 graus e β = 120 graus.
Área do setor circular de ângulo β:
πr².(2π/3)/2π = πr²/3 = 25π/3
Logo, o valor em m² mais aproximado da área do terreno iluminada é:
2(25√3/8 + 25π/3) = 60,625
Resposta:
61
Corrigido pelo DNM
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