В равнобедренном треугольнике со сторонами: a = 0.7737, b = 0.7737, с = 0.7737 высота равна h = 0.67
Ответ:
a=0.7737
b=0.7737
b=0.7737
α°=60°
β°=60°
β°=60°
S = 0.2592
h=0.67
r = 0.2234
R = 0.4467
P = 2.321
Решение:
Сторона:
a =
2h
tg(β°)
=
2·0.67
tg(60°)
=
2·0.67
1.732
= 0.7737
или:
a =
2h
ctg(0.5·α°)
=
2·0.67
ctg(0.5·60°)
=
2·0.67
1.732
= 0.7737
Сторона:
b =
h
sin(β°)
=
0.67
sin(60°)
=
0.67
0.866
= 0.7737
или:
b =
h
cos(0.5·α°)
=
0.67
cos(0.5·60°)
=
0.67
0.866
= 0.7737
Площадь:
S =
a
4
√4· b2 - a2
=
0.7737
4
√4· 0.77372 - 0.77372
=
0.7737
4
√4· 0.59861169 - 0.59861169
=
0.7737
4
√2.39444676 - 0.59861169
=
0.7737
4
√1.79583507
= 0.2592
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
0.7737
2
·√
2·0.7737-0.7737
2·0.7737+0.7737
=0.3869·√0.3333
= 0.2234
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
0.77372
√4·0.77372 - 0.77372
=
0.5986
√2.394 - 0.5986
=
0.5986
1.34
= 0.4467
Периметр:
P = a + 2b
= 0.7737 + 2·0.7737
= 2.321