В треугольнике со сторонами: a = 10, b = 1, с = 9.539, углы равны α° = 114.81°, β° = 5.207°, γ° = 60°
Ответ:
a=10
b=1
c=9.539
α°=114.81°
β°=5.207°
γ°=60°
S = 4.335
ha=0.867
hb=8.67
hc=0.9089
P = 20.54
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √102 + 12 - 2·10·1·cos(60°)
= √100 + 1 - 20·0.5
= √91
= 9.539
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
10
9.539
sin(60°))
= arcsin(1.048·0.866)
= 65.17°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
12+9.5392-102
2·1·9.539
)
= arccos(
1+90.992521-100
19.08
)
= 114.81°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1
9.539
sin(60°))
= arcsin(0.1048·0.866)
= 5.207°
Периметр:
P = a + b + c
= 10 + 1 + 9.539
= 20.54
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.27·(10.27-10)·(10.27-1)·(10.27-9.539)
=√10.27 · 0.27 · 9.27 · 0.731
=√18.790196373
= 4.335
Высота :
ha =
2S
a
=
2 · 4.335
10
= 0.867
hb =
2S
b
=
2 · 4.335
1
= 8.67
hc =
2S
c
=
2 · 4.335
9.539
= 0.9089