В треугольнике со сторонами: a = 4.9, b = 4.9, с = 3.751, углы равны α° = 67.5°, β° = 67.44°, γ° = 45°
Ответ:
a=4.9
b=4.9
c=3.751
α°=67.5°
β°=67.44°
γ°=45°
S = 8.493
ha=3.467
hb=3.467
hc=4.528
P = 13.55
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √4.92 + 4.92 - 2·4.9·4.9·cos(45°)
= √24.01 + 24.01 - 48.02·0.7071
= √14.07
= 3.751
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
4.9
3.751
sin(45°))
= arcsin(1.306·0.7071)
= 67.44°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
4.92+3.7512-4.92
2·4.9·3.751
)
= arccos(
24.01+14.070001-24.01
36.76
)
= 67.5°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
4.9
3.751
sin(45°))
= arcsin(1.306·0.7071)
= 67.44°
Периметр:
P = a + b + c
= 4.9 + 4.9 + 3.751
= 13.55
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√6.776·(6.776-4.9)·(6.776-4.9)·(6.776-3.751)
=√6.776 · 1.876 · 1.876 · 3.025
=√72.1380576224
= 8.493
Высота :
ha =
2S
a
=
2 · 8.493
4.9
= 3.467
hb =
2S
b
=
2 · 8.493
4.9
= 3.467
hc =
2S
c
=
2 · 8.493
3.751
= 4.528