В равнобедренном треугольнике со сторонами: a = 64.2, b = 83.88, с = 83.88, углы равны α° = 45°, β° = 67.5°, γ° = 67.5°
Ответ:
a=64.2
b=83.88
b=83.88
α°=45°
β°=67.5°
β°=67.5°
S = 2487.6
h=77.5
r = 21.45
R = 45.4
P = 231.96
Решение:
Сторона:
b =
h
cos(0.5·α°)
=
77.5
cos(0.5·45°)
=
77.5
0.9239
= 83.88
или:
b = √0.25·a2 + h2
= √0.25·64.22 + 77.52
= √1030.4 + 6006.3
= √7036.7
= 83.89
или:
b =
a
2·sin(0.5·α°)
=
64.2
2·sin(0.5·45°)
=
64.2
0.7654
= 83.88
Угол:
β° =
180-α°
2
=
180-45°
2
= 67.5°
Площадь:
S =
a
4
√4· b2 - a2
=
64.2
4
√4· 83.882 - 64.22
=
64.2
4
√4· 7035.8544 - 4121.64
=
64.2
4
√28143.4176 - 4121.64
=
64.2
4
√24021.7776
= 2487.6
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
64.2
2
·√
2·83.88-64.2
2·83.88+64.2
=32.1·√0.4465
= 21.45
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
83.882
√4·83.882 - 64.22
=
7035.9
√28143.6 - 4121.6
=
7035.9
154.99
= 45.4
Периметр:
P = a + 2b
= 64.2 + 2·83.88
= 231.96