В треугольнике со сторонами: a = 114.24, b = 150, с = 140, углы равны α° = 46.24°, β° = 71.5°, γ° = 62.26°
Ответ:
a=114.24
b=150
c=140
α°=46.24°
β°=71.5°
γ°=62.26°
S = 7583.5
ha=132.76
hb=101.11
hc=108.34
P = 404.24
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
140
150
sin(71.5°))
= arcsin(0.9333·0.9483)
= 62.26°
Угол:
α° = 180 - γ° - β°
= 180 - 62.26° - 71.5°
= 46.24°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √1502 + 1402 - 2·150·140·cos(46.24°)
= √22500 + 19600 - 42000·0.6916
= √13052.8
= 114.25
или:
a = b·
sin(α°)
sin(β°)
= 150·
sin(46.24°)
sin(71.5°)
= 150·
0.7222
0.9483
= 150·0.7616
= 114.24
или:
a = c·
sin(α°)
sin(γ°)
= 140·
sin(46.24°)
sin(62.26°)
= 140·
0.7222
0.8851
= 140·0.816
= 114.24
Периметр:
P = a + b + c
= 114.24 + 150 + 140
= 404.24
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√202.12·(202.12-114.24)·(202.12-150)·(202.12-140)
=√202.12 · 87.88 · 52.12 · 62.12
=√57508917.372209
= 7583.5
Высота :
ha =
2S
a
=
2 · 7583.5
114.24
= 132.76
hb =
2S
b
=
2 · 7583.5
150
= 101.11
hc =
2S
c
=
2 · 7583.5
140
= 108.34