В равнобедренном треугольнике со сторонами: a = 2.064, b = 3.636, с = 3.636, углы равны α° = 33°, β° = 73.5°, γ° = 73.5°
Ответ:
a=2.064
b=3.636
b=3.636
α°=33°
β°=73.5°
β°=73.5°
S = 3.6
h=3.488
r = 0.7708
R = 1.896
P = 9.336
Решение:
Сторона:
a = 2·√S·tg(0.5·α°)
= 2·√3.6·tg(0.5·33°)
= 2·√3.6·0.2962
= 2·√1.066
= 2·1.032
= 2.064
или:
a = 2·√S·ctg(β°)
= 2·√3.6·ctg(73.5°)
= 2·√3.6·0.2962
= 2·√1.066
= 2·1.032
= 2.064
Сторона:
b = √
2S
sin(α°)
= √
2·3.6
sin(33°)
= √
7.2
0.5446
= 3.636
или:
b = √
2S
sin(β°)
= √
2·3.6
sin(180-2·73.5°)
= √
7.2
0.5446
= 3.636
Высота :
h = √b2 - 0.25·a2
= √3.6362 - 0.25·2.0642
= √13.22 - 1.065
= √12.16
= 3.487
или:
h = b·sin(β°)
= 3.636·sin(73.5°)
= 3.636·0.9588
= 3.486
или:
h = b·cos(0.5 · α°)
= 3.636·cos(0.5 · 33°)
= 3.636·0.9588
= 3.486
или:
h = 0.5·a·tan(β°)
= 0.5·2.064·tan(73.5°)
= 0.5·2.064·3.376
= 3.484
или:
h =
0.5·a
tan(0.5 · α°)
=
0.5·2.064
tan(0.5 · 33°)
=
1.032
0.2962
= 3.484
или:
h =
2S
a
=
2 · 3.6
2.064
= 3.488
Радиус вписанной окружности:
r =
a
2
·√
2b-a
2b+a
=
2.064
2
·√
2·3.636-2.064
2·3.636+2.064
=1.032·√0.5578
= 0.7708
Радиус описанной окружности:
R =
b2
√4b2 - a2
=
3.6362
√4·3.6362 - 2.0642
=
13.22
√52.88 - 4.26
=
13.22
6.973
= 1.896
Периметр:
P = a + 2b
= 2.064 + 2·3.636
= 9.336