В равнобедренном треугольнике со сторонами: a = 164, b = 103.86, с = 103.86, углы равны α° = 104.33°, β° = 37.84°, γ° = 37.84°
Ответ:
a=164
b=103.86
b=103.86
α°=104.33°
β°=37.84°
β°=37.84°
S = 5226.8
h=50
r = 28.12
R = 84.62
P = 371.72
Решение:
Сторона:
b =
h
sin(β°)
=
50
sin(37.84°)
=
50
0.6135
= 81.5
или:
b =
h
cos(0.5·α°)
=
50
cos(0.5·104.33°)
=
50
0.6134
= 81.51
или:
b = √0.25·a2 + h2
= √0.25·1642 + 502
= √6724 + 2500
= √9224
= 96.04
или:
b =
a
2·sin(0.5·α°)
=
164
2·sin(0.5·104.33°)
=
164
1.58
= 103.8
или:
b =
a
2·cos(β°)
=
164
2·cos(37.84°)
=
164
1.579
= 103.86
Площадь:
S =
a
4
√4· b2 - a2
=
164
4
√4· 103.862 - 1642
=
164
4
√4· 10786.8996 - 26896
=
164
4
√43147.5984 - 26896
=
164
4
√16251.5984
= 5226.8
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
164
2
·√
2·103.86-164
2·103.86+164
=82·√0.1176
= 28.12
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
103.862
√4·103.862 - 1642
=
10786.9
√43147.6 - 26896
=
10786.9
127.48
= 84.62
Периметр:
P = a + 2b
= 164 + 2·103.86
= 371.72