В треугольнике со сторонами: a = 1.5, b = 1.5, с = 1.826, углы равны α° = 52.51°, β° = 52.51°, γ° = 75°
Ответ:
a=1.5
b=1.5
c=1.826
α°=52.51°
β°=52.51°
γ°=75°
S = 1.087
ha=1.449
hb=1.449
hc=1.191
P = 4.826
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √1.52 + 1.52 - 2·1.5·1.5·cos(75°)
= √2.25 + 2.25 - 4.5·0.2588
= √3.335
= 1.826
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
1.5
1.826
sin(75°))
= arcsin(0.8215·0.9659)
= 52.51°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
1.52+1.8262-1.52
2·1.5·1.826
)
= arccos(
2.25+3.334276-2.25
5.478
)
= 52.51°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1.5
1.826
sin(75°))
= arcsin(0.8215·0.9659)
= 52.51°
Периметр:
P = a + b + c
= 1.5 + 1.5 + 1.826
= 4.826
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√2.413·(2.413-1.5)·(2.413-1.5)·(2.413-1.826)
=√2.413 · 0.913 · 0.913 · 0.587
=√1.180692972239
= 1.087
Высота :
ha =
2S
a
=
2 · 1.087
1.5
= 1.449
hb =
2S
b
=
2 · 1.087
1.5
= 1.449
hc =
2S
c
=
2 · 1.087
1.826
= 1.191