Odpowiedź:
cosα = 3/5
cos²α = (3/5)² = 9/25
1 -sin²α = 9/25
sinα² = 1 - 9/25 = 25/25 -9/25 =16/25
sinα = √(16/25) = 4/5
tgα = sinα/cosα = 4/5 : 3/5 = 4/5 *5/3 = 4/3
a - krawędź podstawy graniastosłupa
H -wysokość graniastosłupa = 8 cm
H/a = tgα
H = a * tgα
a = H : tgα = 8 cm : 4/3 = 8 cm * 3/4 = 2 cm * 3 = 6 cm
Pp - pole podstawy = a²√3/4 = 6² cm² * √3/4 = 36√3/4 cm² = 9√3 cm²
Pb - polo boczne = 3aH = 3 * 6 cm * 8 cm = 144 cm²
Pc - pole całkowite = 2 * Pp + Pb = 2 * 9√3 cm² + 144 cm² =
= 18√3 cm² + 144 cm²= 18(√3 + 8) cm²
