Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √602 + 302 - 2·60·30·cos(30°)
= √3600 + 900 - 3600·0.866
= √1382.4
= 37.18
Высота :
hc = a·sin(β°)
= 60·sin(30°)
= 60·0.5
= 30
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(30°))
= arcsin(1.614·0.5)
= 53.8°
или:
α° = arccos(
)
= arccos(
)
= arccos(
)
= 126.2°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(30°))
= arcsin(0.8069·0.5)
= 23.79°
Периметр:
P = a + b + c
= 60 + 37.18 + 30
= 127.18
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√63.59·(63.59-60)·(63.59-37.18)·(63.59-30)
=√63.59 · 3.59 · 26.41 · 33.59
=√202517.09013839
= 450.02
Высота :
ha =
=
= 15
hb =
=
= 24.21