Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √62 + 62 - 2·6·6·cos(45°)
= √36 + 36 - 72·0.7071
= √21.09
= 4.592
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(45°))
= arcsin(1.307·0.7071)
= 67.54°
или:
α° = arccos(
)
= arccos(
)
= arccos(
)
= 67.5°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(45°))
= arcsin(1.307·0.7071)
= 67.54°
Периметр:
P = a + b + c
= 6 + 6 + 4.592
= 16.59
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√8.296·(8.296-6)·(8.296-6)·(8.296-4.592)
=√8.296 · 2.296 · 2.296 · 3.704
=√161.98824074854
= 12.73
Высота :
ha =
=
= 4.243
hb =
=
= 4.243
hc =
=
= 5.544