В равнобедренном треугольнике со сторонами: a = 21.6, b = 85.58, с = 85.58 высота равна h = 83.5
Ответ:
a=21.6
b=85.58
b=85.58
α°=14.5°
β°=82.75°
β°=82.75°
S = 916.87
h=83.5
r = 9.513
R = 43.14
P = 192.76
Решение:
Сторона:
b =
h
cos(0.5·α°)
=
83.5
cos(0.5·14.5°)
=
83.5
0.992
= 84.17
или:
b = √0.25·a2 + h2
= √0.25·21.62 + 83.52
= √116.64 + 6972.3
= √7088.9
= 84.2
или:
b =
a
2·sin(0.5·α°)
=
21.6
2·sin(0.5·14.5°)
=
21.6
0.2524
= 85.58
Угол:
β° =
180-α°
2
=
180-14.5°
2
= 82.75°
Площадь:
S =
a
4
√4· b2 - a2
=
21.6
4
√4· 85.582 - 21.62
=
21.6
4
√4· 7323.9364 - 466.56
=
21.6
4
√29295.7456 - 466.56
=
21.6
4
√28829.1856
= 916.87
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
21.6
2
·√
2·85.58-21.6
2·85.58+21.6
=10.8·√0.7759
= 9.513
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
85.582
√4·85.582 - 21.62
=
7323.9
√29295.6 - 466.56
=
7323.9
169.79
= 43.14
Периметр:
P = a + 2b
= 21.6 + 2·85.58
= 192.76