В треугольнике со сторонами: a = 71.59, b = 30, с = 60, углы равны α° = 100°, β° = 24.38°, γ° = 55.63°
Ответ:
a=71.59
b=30
c=60
α°=100°
β°=24.38°
γ°=55.63°
S = 886.75
ha=24.77
hb=59.12
hc=29.56
P = 161.59
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √302 + 602 - 2·30·60·cos(100°)
= √900 + 3600 - 3600·-0.1736
= √5125
= 71.59
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
30
71.59
sin(100°))
= arcsin(0.4191·0.9848)
= 24.38°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
60
71.59
sin(100°))
= arcsin(0.8381·0.9848)
= 55.63°
Периметр:
P = a + b + c
= 71.59 + 30 + 60
= 161.59
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√80.8·(80.8-71.59)·(80.8-30)·(80.8-60)
=√80.8 · 9.21 · 50.8 · 20.8
=√786317.67552
= 886.75
Высота :
ha =
2S
a
=
2 · 886.75
71.59
= 24.77
hb =
2S
b
=
2 · 886.75
30
= 59.12
hc =
2S
c
=
2 · 886.75
60
= 29.56