В треугольнике со сторонами: a = 7, b = 5, с = 8.95, углы равны α° = 51.18°, β° = 33.82°, γ° = 95°
Ответ:
a=7
b=5
c=8.95
α°=51.18°
β°=33.82°
γ°=95°
S = 17.49
ha=4.997
hb=6.996
hc=3.908
P = 20.95
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √72 + 52 - 2·7·5·cos(95°)
= √49 + 25 - 70·-0.08716
= √80.1
= 8.95
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
7
8.95
sin(95°))
= arcsin(0.7821·0.9962)
= 51.18°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
52+8.952-72
2·5·8.95
)
= arccos(
25+80.1025-49
89.5
)
= 51.18°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5
8.95
sin(95°))
= arcsin(0.5587·0.9962)
= 33.82°
Периметр:
P = a + b + c
= 7 + 5 + 8.95
= 20.95
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.48·(10.48-7)·(10.48-5)·(10.48-8.95)
=√10.48 · 3.48 · 5.48 · 1.53
=√305.78242176
= 17.49
Высота :
ha =
2S
a
=
2 · 17.49
7
= 4.997
hb =
2S
b
=
2 · 17.49
5
= 6.996
hc =
2S
c
=
2 · 17.49
8.95
= 3.908