В равнобедренном треугольнике со сторонами: a = 4.055, b = 2.29, с = 2.29, углы равны α° = 124.6°, β° = 27.7°, γ° = 27.7°
Ответ:
a=4.055
b=2.29
b=2.29
α°=124.6°
β°=27.7°
β°=27.7°
S = 2.158
h=1.165
r = 0.5001
R = 2.461
P = 8.635
Решение:
Сторона:
b =
h
cos(0.5·α°)
=
1.165
cos(0.5·124.6°)
=
1.165
0.4648
= 2.506
или:
b = √0.25·a2 + h2
= √0.25·4.0552 + 1.1652
= √4.111 + 1.357
= √5.468
= 2.338
или:
b =
a
2·sin(0.5·α°)
=
4.055
2·sin(0.5·124.6°)
=
4.055
1.771
= 2.29
Угол:
β° =
180-α°
2
=
180-124.6°
2
= 27.7°
Площадь:
S =
a
4
√4· b2 - a2
=
4.055
4
√4· 2.292 - 4.0552
=
4.055
4
√4· 5.2441 - 16.443025
=
4.055
4
√20.9764 - 16.443025
=
4.055
4
√4.533375
= 2.158
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
4.055
2
·√
2·2.29-4.055
2·2.29+4.055
=2.028·√0.0608
= 0.5001
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
2.292
√4·2.292 - 4.0552
=
5.244
√20.98 - 16.44
=
5.244
2.131
= 2.461
Периметр:
P = a + 2b
= 4.055 + 2·2.29
= 8.635