В треугольнике со сторонами: a = 5.7, b = 1.5, с = 5.894, углы равны α° = 75.26°, β° = 14.74°, γ° = 90°
Ответ:
a=5.7
b=1.5
c=5.894
α°=75.26°
β°=14.74°
γ°=90°
S = 4.275
ha=1.5
hb=5.7
hc=1.451
P = 13.09
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.72 + 1.52 - 2·5.7·1.5·cos(90°)
= √32.49 + 2.25 - 17.1·0
= √34.74
= 5.894
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5.7
5.894
sin(90°))
= arcsin(0.9671·1)
= 75.26°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
1.52+5.8942-5.72
2·1.5·5.894
)
= arccos(
2.25+34.739236-32.49
17.68
)
= 75.26°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1.5
5.894
sin(90°))
= arcsin(0.2545·1)
= 14.74°
Периметр:
P = a + b + c
= 5.7 + 1.5 + 5.894
= 13.09
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√6.547·(6.547-5.7)·(6.547-1.5)·(6.547-5.894)
=√6.547 · 0.847 · 5.047 · 0.653
=√18.275624963519
= 4.275
Высота :
ha =
2S
a
=
2 · 4.275
5.7
= 1.5
hb =
2S
b
=
2 · 4.275
1.5
= 5.7
hc =
2S
c
=
2 · 4.275
5.894
= 1.451