В треугольнике со сторонами: a = 88, b = 122, с = 150.43 высоты равны ha = 122.02, hb = 88.01, hc = 71.38
Ответ:
a=88
b=122
c=150.43
α°=35.8°
β°=54.19°
γ°=90°
S = 5368.9
ha=122.02
hb=88.01
hc=71.38
P = 360.43
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √882 + 1222 - 2·88·122·cos(90°)
= √7744 + 14884 - 21472·0
= √22628
= 150.43
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
88
150.43
sin(90°))
= arcsin(0.585·1)
= 35.8°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
1222+150.432-882
2·122·150.43
)
= arccos(
14884+22629.1849-7744
36704.9
)
= 35.8°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
122
150.43
sin(90°))
= arcsin(0.811·1)
= 54.19°
Периметр:
P = a + b + c
= 88 + 122 + 150.43
= 360.43
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√180.22·(180.22-88)·(180.22-122)·(180.22-150.43)
=√180.22 · 92.22 · 58.22 · 29.79
=√28825098.999884
= 5368.9
Высота :
ha =
2S
a
=
2 · 5368.9
88
= 122.02
hb =
2S
b
=
2 · 5368.9
122
= 88.01
hc =
2S
c
=
2 · 5368.9
150.43
= 71.38