В треугольнике со сторонами: a = 10, b = 3, с = 8.888, углы равны α° = 103.01°, β° = 16.99°, γ° = 60°
Ответ:
a=10
b=3
c=8.888
α°=103.01°
β°=16.99°
γ°=60°
S = 12.94
ha=2.588
hb=8.627
hc=2.912
P = 21.89
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √102 + 32 - 2·10·3·cos(60°)
= √100 + 9 - 60·0.5
= √79
= 8.888
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
10
8.888
sin(60°))
= arcsin(1.125·0.866)
= 76.97°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
32+8.8882-102
2·3·8.888
)
= arccos(
9+78.996544-100
53.33
)
= 103.01°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
3
8.888
sin(60°))
= arcsin(0.3375·0.866)
= 16.99°
Периметр:
P = a + b + c
= 10 + 3 + 8.888
= 21.89
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.94·(10.94-10)·(10.94-3)·(10.94-8.888)
=√10.94 · 0.94 · 7.94 · 2.052
=√167.549460768
= 12.94
Высота :
ha =
2S
a
=
2 · 12.94
10
= 2.588
hb =
2S
b
=
2 · 12.94
3
= 8.627
hc =
2S
c
=
2 · 12.94
8.888
= 2.912