В равнобедренном треугольнике со сторонами: a = 171.59, b = 197.5, с = 197.5, углы равны α° = 51.5°, β° = 64.25°, γ° = 64.25°
Ответ:
a=171.59
b=197.5
b=197.5
α°=51.5°
β°=64.25°
β°=64.25°
S = 15262.2
h=177.89
r = 53.88
R = 109.64
P = 566.59
Решение:
Сторона:
a = 2b·sin(0.5·α°)
= 2·197.5·sin(0.5·51.5°)
= 2·197.5·0.4344
= 171.59
Угол:
β° =
180-α°
2
=
180-51.5°
2
= 64.25°
Высота :
h = b·cos(0.5 · α°)
= 197.5·cos(0.5 · 51.5°)
= 197.5·0.9007
= 177.89
Площадь:
S =
a
4
√4· b2 - a2
=
171.59
4
√4· 197.52 - 171.592
=
171.59
4
√4· 39006.25 - 29443.1281
=
171.59
4
√156025 - 29443.1281
=
171.59
4
√126581.8719
= 15262.2
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
171.59
2
·√
2·197.5-171.59
2·197.5+171.59
=85.8·√0.3943
= 53.88
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
197.52
√4·197.52 - 171.592
=
39006.3
√156025.2 - 29443.1
=
39006.3
355.78
= 109.64
Периметр:
P = a + 2b
= 171.59 + 2·197.5
= 566.59