В равнобедренном треугольнике со сторонами: a = 10.0, b = 5.314, с = 5.314, углы равны α° = 140.41°, β° = 19.79°, γ° = 19.79°
Ответ:
a=10.0
b=5.314
b=5.314
α°=140.41°
β°=19.79°
β°=19.79°
S = 8.998
h=1.80
r = 0.8724
R = 7.844
P = 20.63
Решение:
Сторона:
b = √0.25·a2 + h2
= √0.25·10.02 + 1.802
= √25 + 3.24
= √28.24
= 5.314
Угол:
α° = 2·arcsin
a
2b
= 2·arcsin
10.0
2·5.314
= 140.41°
Угол:
β° = arccos
a
2b
= 2·arccos
10.0
5.314
= 19.79°
Площадь:
S =
a
4
√4· b2 - a2
=
10.0
4
√4· 5.3142 - 10.02
=
10.0
4
√4· 28.238596 - 100
=
10.0
4
√112.954384 - 100
=
10.0
4
√12.954384
= 8.998
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
10.0
2
·√
2·5.314-10.0
2·5.314+10.0
=5·√0.03044
= 0.8724
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
5.3142
√4·5.3142 - 10.02
=
28.24
√112.96 - 100
=
28.24
3.6
= 7.844
Периметр:
P = a + 2b
= 10.0 + 2·5.314
= 20.63