В треугольнике со сторонами: a = 170, b = 182.75, с = 140, углы равны α° = 61.91°, β° = 71.5°, γ° = 46.59°
Ответ:
a=170
b=182.75
c=140
α°=61.91°
β°=71.5°
γ°=46.59°
S = 11286.3
ha=132.78
hb=123.52
hc=161.21
P = 492.75
Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √1702 + 1402 - 2·170·140·cos(71.5°)
= √28900 + 19600 - 47600·0.3173
= √33396.5
= 182.75
Высота :
hc = a·sin(β°)
= 170·sin(71.5°)
= 170·0.9483
= 161.21
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
170
182.75
sin(71.5°))
= arcsin(0.9302·0.9483)
= 61.9°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
182.752+1402-1702
2·182.75·140
)
= arccos(
33397.5625+19600-28900
51170
)
= 61.91°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
140
182.75
sin(71.5°))
= arcsin(0.7661·0.9483)
= 46.59°
Периметр:
P = a + b + c
= 170 + 182.75 + 140
= 492.75
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√246.38·(246.38-170)·(246.38-182.75)·(246.38-140)
=√246.38 · 76.38 · 63.63 · 106.38
=√127381692.25232
= 11286.3
Высота :
ha =
2S
a
=
2 · 11286.3
170
= 132.78
hb =
2S
b
=
2 · 11286.3
182.75
= 123.52