Odpowiedź:
5/t = sin60° = √3/2
5 = t * √3/2
t = 5 : √3/2 = 5 * 2/√3 = 10/√3 =10√3/3 [j]
z/t = cos60° = 1/2
z = t * 1/2 = 10√3/3 * 1/2 = 10√3/6 = 5√3/3 [j]
5/x = sin45° = √2/2
5 = x * √2/2
x = 5 : √2/2 = 5 * 2√2 = 10/√2 = 10√2/2 = 5√2 [j]
y/x = cos45° = √2/2
y = x * √2/2 = 5√2 * √2/2 = 5 * 2/2 = 5 [j]
o - obwód = x + y + z + t = 5√2 + 5 + 5√3/3 + 10√3/3 =
= 5√2 + 15√3/3 + 5 = 5√2 + 5√3 + 5 = 5(√2 + √3 + 1) [j]
P - pole trójkąta = 1/2 *(z + y) * 5 = 1/2 * (5√3/3 + 5) * 5 =
= (5√3/6 + 5/2) * 5 = 25√3/6 + 25/2 = (25√3/6 + 75/6) =
= (25√3+ 75)/6 = 25(√3 +3)/6 = 4,1(6) * (√3 + 3) [j²]
[j] - znaczy włąściwa jednostka
