Odpowiedź:
zad 5
5/z = tg60° = √3
5 = z * √3
z = 5/√3 = 5√3/3
5/t = sin60° = √3/2
5 = t * √3/2
t = 5 : √3/2 = 5 * 2/√3 = 10/√3 = 10√3/3
5/y = tg45° = 1
5 = y * 1 = y
y = 5
5/x = sin45° = √2/2
5 = x * √2/2
x = 5 : √2/2 = 5 * 2/√2 = 10/√2 = 10√2/2
o- obwód trójkąta = t + x + y + z = 10√3/3 + 10√2/2 + 5 + 5√3/3 =
= 15√3/3 + 10√2/2 + 5 = 5√3 + 5√2 + 5 = 5(√3 + √2 + 1)
P - pole trójkąta = 1/2(z+y) * 5 = 1/2 * (5√3/3 + 5) * 5 =
= 1/2 * [(5√3 + 15)/3] * 5 = [5 * 5(√3 + 3)]/6 = 25(√3 + 3)/6 =
= 8,(3) * (√3 + 3)
