В треугольнике со сторонами: a = 251.93, b = 247.6, с = 350, углы равны α° = 46.03°, β° = 45°, γ° = 88.97°
Ответ:
a=251.93
b=247.6
c=350
α°=46.03°
β°=45°
γ°=88.97°
S = 31185.9
ha=247.58
hb=251.91
hc=178.21
P = 849.53
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
350
247.6
sin(45°))
= arcsin(1.414·0.7071)
= 88.97°
Угол:
α° = 180 - γ° - β°
= 180 - 88.97° - 45°
= 46.03°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √247.62 + 3502 - 2·247.6·350·cos(46.03°)
= √61305.8 + 122500 - 173320·0.6943
= √63469.7
= 251.93
или:
a = b·
sin(α°)
sin(β°)
= 247.6·
sin(46.03°)
sin(45°)
= 247.6·
0.7197
0.7071
= 247.6·1.018
= 252.06
или:
a = c·
sin(α°)
sin(γ°)
= 350·
sin(46.03°)
sin(88.97°)
= 350·
0.7197
0.9998
= 350·0.7198
= 251.93
Периметр:
P = a + b + c
= 251.93 + 247.6 + 350
= 849.53
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√424.77·(424.77-251.93)·(424.77-247.6)·(424.77-350)
=√424.77 · 172.84 · 177.17 · 74.77
=√972558334.43512
= 31185.9
Высота :
ha =
2S
a
=
2 · 31185.9
251.93
= 247.58
hb =
2S
b
=
2 · 31185.9
247.6
= 251.91
hc =
2S
c
=
2 · 31185.9
350
= 178.21