Решение:
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(36.53°))
= arcsin(0.6222·0.5952)
= 21.74°
Высота :
hc = a·sin(β°)
= 2.8·sin(36.53°)
= 2.8·0.5952
= 1.667
Угол:
γ° = 180 - α° - β°
= 180 - 21.74° - 36.53°
= 121.73°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √2.82 + 4.52 - 2·2.8·4.5·cos(121.73°)
= √7.84 + 20.25 - 25.2·-0.5259
= √41.34
= 6.43
или:
c = a·
= 2.8·
= 2.8·
= 2.8·2.296
= 6.429
или:
c = b·
= 4.5·
= 4.5·
= 4.5·1.429
= 6.431
Периметр:
P = a + b + c
= 2.8 + 4.5 + 6.431
= 13.73
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√6.866·(6.866-2.8)·(6.866-4.5)·(6.866-6.431)
=√6.866 · 4.066 · 2.366 · 0.435
=√28.73261612676
= 5.36
hb =
=
= 2.382