Question

Zadanie w załączniku. Z ubiegłej matury

Answer 1

Mamy dane:
b = 80 cm
α = 30
P = ? [cm²]

P = 0,5a*h

α + 2β = 180

2β = 180 - α

2β = 180 - 30

2β = 150/ :2

β = 75

h/b = sinβ /*b

h = b*sinβ

(a/2)/b = cosβ /*b

a/2 = b*cosβ / *2

a = 2b*cosβ

P = 0,5*(2bcosβ)*bsinβ

P = 0,5b²(2sinβcosβ)

P = 0,5b²sin2β

P = 0,5(80 cm)²sin(2*75)

P = 0,5*(6400 cm²)sin150

P = (3200 cm²)sin(180 - 30)

P = (3200 cm²)sin30

P = 0,5*3200 cm²

P = 1600 cm²

Odp; Pole powierzchni zacieniowanego latawca wynosi 1600 cm²