Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √412 + 412 - 2·41·41·cos(144°)
= √1681 + 1681 - 3362·-0.809
= √6081.9
= 77.99
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(144°))
= arcsin(0.5257·0.5878)
= 18°
или:
α° = arccos(
)
= arccos(
)
= arccos(
1681+6082.4401-1681
6395.2
)
= 17.99°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(144°))
= arcsin(0.5257·0.5878)
= 18°
Периметр:
P = a + b + c
= 41 + 41 + 77.99
= 159.99
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√80·(80-41)·(80-41)·(80-77.99)
=√80 · 39 · 39 · 2.01
=√244576.8
= 494.55
Высота :
ha =
=
= 24.12
hb =
=
= 24.12
hc =
=
= 12.68