В равнобедренном треугольнике со сторонами: a = 2.346, b = 3.332, с = 3.332, углы равны α° = 41.219°, β° = 69.39°, γ° = 69.39°
Ответ:
a=2.346
b=3.332
b=3.332
α°=41.219°
β°=69.39°
β°=69.39°
S = 3.658
h=3.119
r = 0.812
R = 1.78
P = 9.01
Решение:
Сторона:
b =
a
2·sin(0.5·α°)
=
2.346
2·sin(0.5·41.219°)
=
2.346
0.704
= 3.332
или:
b =
a
2·cos(β°)
=
2.346
2·cos(69.39°)
=
2.346
0.704
= 3.332
Высота :
h = 0.5·a·tan(β°)
= 0.5·2.346·tan(69.39°)
= 0.5·2.346·2.659
= 3.119
или:
h =
0.5·a
tan(0.5 · α°)
=
0.5·2.346
tan(0.5 · 41.219°)
=
1.173
0.3761
= 3.119
Площадь:
S =
a
4
√4· b2 - a2
=
2.346
4
√4· 3.3322 - 2.3462
=
2.346
4
√4· 11.102224 - 5.503716
=
2.346
4
√44.408896 - 5.503716
=
2.346
4
√38.90518
= 3.658
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
2.346
2
·√
2·3.332-2.346
2·3.332+2.346
=1.173·√0.4792
= 0.812
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
3.3322
√4·3.3322 - 2.3462
=
11.1
√44.4 - 5.504
=
11.1
6.237
= 1.78
Периметр:
P = a + 2b
= 2.346 + 2·3.332
= 9.01