Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √12 + 0.752 - 2·1·0.75·cos(60°)
= √1 + 0.5625 - 1.5·0.5
= √0.8125
= 0.9014
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(60°))
= arcsin(1.109·0.866)
= 73.82°
или:
α° = arccos(
)
= arccos(
0.752+0.90142-12
2·0.75·0.9014
)
= arccos(
)
= 73.9°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(60°))
= arcsin(0.832·0.866)
= 46.1°
Периметр:
P = a + b + c
= 1 + 0.75 + 0.9014
= 2.651
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√1.326·(1.326-1)·(1.326-0.75)·(1.326-0.9014)
=√1.326 · 0.326 · 0.576 · 0.4246
=√0.1057215684096
= 0.3251
Высота :
ha =
=
= 0.6502
hb =
=
= 0.8669
hc =
=
= 0.7213