Решение:
Сторона:
c = a·
= 18·
= 18·
= 18·1.732
= 31.18
Угол:
β° = 180 - γ° - α°
= 180 - 60° - 30°
= 90°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √182 + 31.182 - 2·18·31.18·cos(90°)
= √324 + 972.19 - 1122.5·0
= √1296.2
= 36
или:
b = a·
= 18·
= 18·
= 18·2
= 36
или:
b = c·
= 31.18·
= 31.18·
= 31.18·1.155
= 36.01
Высота :
hc = a·sin(β°)
= 18·sin(90°)
= 18·1
= 18
Периметр:
P = a + b + c
= 18 + 36.01 + 31.18
= 85.19
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√42.6·(42.6-18)·(42.6-36.01)·(42.6-31.18)
=√42.6 · 24.6 · 6.59 · 11.42
=√78867.164088
= 280.83
Высота :
ha =
=
= 31.2
hb =
=
= 15.6