Question

Dado um triângulo retângulo cuja hipotenusa vale 13 cm e os catetos 12 cm e 5 cm, Quais são os valores dos ângulos agudos?

Answer 1

Para visualizar melhor, um esboço do triangulo

                  A
                   |                                           Triangulo ABC reto em C
                   |                                                           AC = 12
                   |                                                           CB = 5
                   |                                                           AB = 13
                   |                                           Comprovar se ABC é retangulo
                  C               B                         Aplicando Teorema de Pitágoras
                                                                 (13)² = (12)² + (5)²
                                                                   169 = 144 + 25
                                                                   169 = 169    VERIFICAÇÃO OK
          Para o ângulo ABC
                    tag(ABC) = (AC)/(CB)
                                    = 12/5
                    tag(ABC) = 2,4
         Logo
                    ABC = arc tag (2,4)
                            = 67,38°
                                                             Ângulo ABC = 67° 23'
                                                             Ângulo BAC = 22° 23'
                                                                            [90 - (67° 23')] = 22°37'