В равнобедренном треугольнике со сторонами: a = 1.45, b = 2.411, с = 2.411, углы равны α° = 35°, β° = 72.5°, γ° = 72.5°
Ответ:
a=1.45
b=2.411
b=2.411
α°=35°
β°=72.5°
β°=72.5°
S = 1.667
h=2.0
r = 0.5316
R = 1.264
P = 6.272
Решение:
Сторона:
b =
h
cos(0.5·α°)
=
2.0
cos(0.5·35°)
=
2.0
0.9537
= 2.097
или:
b = √0.25·a2 + h2
= √0.25·1.452 + 2.02
= √0.5256 + 4
= √4.526
= 2.127
или:
b =
a
2·sin(0.5·α°)
=
1.45
2·sin(0.5·35°)
=
1.45
0.6014
= 2.411
Угол:
β° =
180-α°
2
=
180-35°
2
= 72.5°
Площадь:
S =
a
4
√4· b2 - a2
=
1.45
4
√4· 2.4112 - 1.452
=
1.45
4
√4· 5.812921 - 2.1025
=
1.45
4
√23.251684 - 2.1025
=
1.45
4
√21.149184
= 1.667
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
1.45
2
·√
2·2.411-1.45
2·2.411+1.45
=0.725·√0.5376
= 0.5316
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
2.4112
√4·2.4112 - 1.452
=
5.813
√23.25 - 2.103
=
5.813
4.599
= 1.264
Периметр:
P = a + 2b
= 1.45 + 2·2.411
= 6.272