В треугольнике со сторонами: a = 5.5, b = 5.5, с = 7.778, углы равны α° = 45°, β° = 45°, γ° = 90°
Ответ:
a=5.5
b=5.5
c=7.778
α°=45°
β°=45°
γ°=90°
S = 15.12
ha=5.498
hb=5.498
hc=3.888
P = 18.78
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.52 + 5.52 - 2·5.5·5.5·cos(90°)
= √30.25 + 30.25 - 60.5·0
= √60.5
= 7.778
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5.5
7.778
sin(90°))
= arcsin(0.7071·1)
= 45°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.52+7.7782-5.52
2·5.5·7.778
)
= arccos(
30.25+60.497284-30.25
85.56
)
= 45°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.5
7.778
sin(90°))
= arcsin(0.7071·1)
= 45°
Периметр:
P = a + b + c
= 5.5 + 5.5 + 7.778
= 18.78
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√9.389·(9.389-5.5)·(9.389-5.5)·(9.389-7.778)
=√9.389 · 3.889 · 3.889 · 1.611
=√228.76562453896
= 15.12
Высота :
ha =
2S
a
=
2 · 15.12
5.5
= 5.498
hb =
2S
b
=
2 · 15.12
5.5
= 5.498
hc =
2S
c
=
2 · 15.12
7.778
= 3.888