В треугольнике со сторонами: a = 2817.6, b = 1200, с = 2400, углы равны α° = 97.31°, β° = 25°, γ° = 57.69°
Ответ:
a=2817.6
b=1200
c=2400
α°=97.31°
β°=25°
γ°=57.69°
S = 1428103
ha=1013.7
hb=2380.2
hc=1190.1
P = 6417.6
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
2400
1200
sin(25°))
= arcsin(2·0.4226)
= 57.69°
Угол:
α° = 180 - γ° - β°
= 180 - 57.69° - 25°
= 97.31°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √12002 + 24002 - 2·1200·2400·cos(97.31°)
= √1440000 + 5760000 - 5760000·-0.1272
= √7932672
= 2816.5
или:
a = b·
sin(α°)
sin(β°)
= 1200·
sin(97.31°)
sin(25°)
= 1200·
0.9919
0.4226
= 1200·2.347
= 2816.4
или:
a = c·
sin(α°)
sin(γ°)
= 2400·
sin(97.31°)
sin(57.69°)
= 2400·
0.9919
0.8452
= 2400·1.174
= 2817.6
Периметр:
P = a + b + c
= 2817.6 + 1200 + 2400
= 6417.6
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3208.8·(3208.8-2817.6)·(3208.8-1200)·(3208.8-2400)
=√3208.8 · 391.2 · 2008.8 · 808.8
=√2039479467359.8
= 1428103
Высота :
ha =
2S
a
=
2 · 1428103
2817.6
= 1013.7
hb =
2S
b
=
2 · 1428103
1200
= 2380.2
hc =
2S
c
=
2 · 1428103
2400
= 1190.1