Question

una lampara de emergencia tiene un alcanse de 20 mts. y produce una luz en un angulo de 100, aproximadamente cuantos metros cuadrados ilumina?

Answer 1

Darling,
Un esbozo del sistema para mejor visualizar
                                      
                                        A
                                                        OP = 20 m
                                                        angulo AOB = 100°
                     O................P
                                                        en el triangulo APO, recto en P
                                                        angulo AOP = 50°
                                        B              angulo OAP = 40°

                                                 Aplicando ley de senos
                                                          20/(sen 40°) = AP/(sen 50°)
                                                          20/(0.6428) = AP/(0.7660)
                                                           Efectuando
                                                           AP = 23.83
Area iluminada = area triangulo AOB
                         = 2(area triangulo APO) {triang APO = triang BPO)

                         = 2[1/2(AP * OP)]
                         = (23.83)*(20)
                         = 476.6

                                          ILUMINA 477 m^2 (aproximado por exceso)