В равнобедренном треугольнике со сторонами: a = 3.5, b = 2.006, с = 2.006, углы равны α° = 121.47°, β° = 29.26°, γ° = 29.26°
Ответ:
a=3.5
b=2.006
b=2.006
α°=121.47°
β°=29.26°
β°=29.26°
S = 1.716
h=0.98
r = 0.4569
R = 2.051
P = 7.512
Решение:
Сторона:
b = √0.25·a2 + h2
= √0.25·3.52 + 0.982
= √3.063 + 0.9604
= √4.023
= 2.006
Угол:
α° = 2·arcsin
a
2b
= 2·arcsin
3.5
2·2.006
= 121.47°
Угол:
β° = arccos
a
2b
= 2·arccos
3.5
2.006
= 29.26°
Площадь:
S =
a
4
√4· b2 - a2
=
3.5
4
√4· 2.0062 - 3.52
=
3.5
4
√4· 4.024036 - 12.25
=
3.5
4
√16.096144 - 12.25
=
3.5
4
√3.846144
= 1.716
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
3.5
2
·√
2·2.006-3.5
2·2.006+3.5
=1.75·√0.06816
= 0.4569
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
2.0062
√4·2.0062 - 3.52
=
4.024
√16.1 - 12.25
=
4.024
1.962
= 2.051
Периметр:
P = a + 2b
= 3.5 + 2·2.006
= 7.512