В равнобедренном треугольнике со сторонами: a = 5.94, b = 4.082, с = 4.082, углы равны α° = 93.37°, β° = 43.32°, γ° = 43.32°
Ответ:
a=5.94
b=4.082
b=4.082
α°=93.37°
β°=43.32°
β°=43.32°
S = 8.317
h=2.8
r = 1.179
R = 2.975
P = 14.1
Решение:
Сторона:
b = √0.25·a2 + h2
= √0.25·5.942 + 2.82
= √8.821 + 7.84
= √16.66
= 4.082
Угол:
α° = 2·arcsin
a
2b
= 2·arcsin
5.94
2·4.082
= 93.37°
Угол:
β° = arccos
a
2b
= 2·arccos
5.94
4.082
= 43.32°
Площадь:
S =
a
4
√4· b2 - a2
=
5.94
4
√4· 4.0822 - 5.942
=
5.94
4
√4· 16.662724 - 35.2836
=
5.94
4
√66.650896 - 35.2836
=
5.94
4
√31.367296
= 8.317
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
5.94
2
·√
2·4.082-5.94
2·4.082+5.94
=2.97·√0.1577
= 1.179
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
4.0822
√4·4.0822 - 5.942
=
16.66
√66.64 - 35.28
=
16.66
5.6
= 2.975
Периметр:
P = a + 2b
= 5.94 + 2·4.082
= 14.1