В треугольнике со сторонами: a = 2.5, b = 2.5, с = 2.5, углы равны α° = 60°, β° = 60°, γ° = 60°
Ответ:
a=2.5
b=2.5
c=2.5
α°=60°
β°=60°
γ°=60°
S = 2.706
ha=2.165
hb=2.165
hc=2.165
P = 7.5
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √2.52 + 2.52 - 2·2.5·2.5·cos(60°)
= √6.25 + 6.25 - 12.5·0.5
= √6.25
= 2.5
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
2.5
2.5
sin(60°))
= arcsin(1·0.866)
= 60°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
2.52+2.52-2.52
2·2.5·2.5
)
= arccos(
6.25+6.25-6.25
12.5
)
= 60°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
2.5
2.5
sin(60°))
= arcsin(1·0.866)
= 60°
Периметр:
P = a + b + c
= 2.5 + 2.5 + 2.5
= 7.5
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.75·(3.75-2.5)·(3.75-2.5)·(3.75-2.5)
=√3.75 · 1.25 · 1.25 · 1.25
=√7.32421875
= 2.706
Высота :
ha =
2S
a
=
2 · 2.706
2.5
= 2.165
hb =
2S
b
=
2 · 2.706
2.5
= 2.165
hc =
2S
c
=
2 · 2.706
2.5
= 2.165