В треугольнике со сторонами: a = 871.78, b = 600, с = 1000, углы равны α° = 60°, β° = 36.58°, γ° = 83.36°
Ответ:
a=871.78
b=600
c=1000
α°=60°
β°=36.58°
γ°=83.36°
S = 259819.8
ha=596.07
hb=866.07
hc=519.64
P = 2471.8
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √6002 + 10002 - 2·600·1000·cos(60°)
= √360000 + 1000000 - 1200000·0.5
= √760000
= 871.78
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
600
871.78
sin(60°))
= arcsin(0.6882·0.866)
= 36.58°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
1000
871.78
sin(60°))
= arcsin(1.147·0.866)
= 83.36°
Периметр:
P = a + b + c
= 871.78 + 600 + 1000
= 2471.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√1235.9·(1235.9-871.78)·(1235.9-600)·(1235.9-1000)
=√1235.9 · 364.12 · 635.9 · 235.9
=√67506350840.15
= 259819.8
Высота :
ha =
2S
a
=
2 · 259819.8
871.78
= 596.07
hb =
2S
b
=
2 · 259819.8
600
= 866.07
hc =
2S
c
=
2 · 259819.8
1000
= 519.64