Решение:
Сторона:
b = c·
= 7.071·
= 7.071·
= 7.071·0.7071
= 5
Угол:
α° = 180 - γ° - β°
= 180 - 45° - 30°
= 105°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √52 + 7.0712 - 2·5·7.071·cos(105°)
= √25 + 50 - 70.71·-0.2588
= √93.3
= 9.659
или:
a = b·
= 5·
= 5·
= 5·1.932
= 9.66
или:
a = c·
= 7.071·
= 7.071·
= 7.071·1.366
= 9.659
Периметр:
P = a + b + c
= 9.659 + 5 + 7.071
= 21.73
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√10.87·(10.87-9.659)·(10.87-5)·(10.87-7.071)
=√10.87 · 1.211 · 5.87 · 3.799
=√293.5493222641
= 17.13
Высота :
ha =
=
= 3.547
hb =
=
= 6.852
hc =
=
= 4.845