В треугольнике со сторонами: a = 392.17, b = 370, с = 130 высоты равны ha = 122.66, hb = 130.01, hc = 370.03
Ответ:
a=392.17
b=370
c=130
α°=90°
β°=70.65°
γ°=19.36°
S = 24052.2
ha=122.66
hb=130.01
hc=370.03
P = 892.17
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √3702 + 1302 - 2·370·130·cos(90°)
= √136900 + 16900 - 96200·0
= √153800
= 392.17
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
370
392.17
sin(90°))
= arcsin(0.9435·1)
= 70.65°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
130
392.17
sin(90°))
= arcsin(0.3315·1)
= 19.36°
Периметр:
P = a + b + c
= 392.17 + 370 + 130
= 892.17
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√446.09·(446.09-392.17)·(446.09-370)·(446.09-130)
=√446.09 · 53.92 · 76.09 · 316.09
=√578509788.73188
= 24052.2
Высота :
ha =
2S
a
=
2 · 24052.2
392.17
= 122.66
hb =
2S
b
=
2 · 24052.2
370
= 130.01
hc =
2S
c
=
2 · 24052.2
130
= 370.03