В треугольнике со сторонами: a = 13.65, b = 10.6, с = 8.6 высоты равны ha = 6.69, hb = 8.615, hc = 10.62
Ответ:
a=13.65
b=10.6
c=8.6
α°=90°
β°=50.95°
γ°=39.05°
S = 45.66
ha=6.69
hb=8.615
hc=10.62
P = 32.85
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √10.62 + 8.62 - 2·10.6·8.6·cos(90°)
= √112.36 + 73.96 - 182.32·0
= √186.32
= 13.65
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
10.6
13.65
sin(90°))
= arcsin(0.7766·1)
= 50.95°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
8.6
13.65
sin(90°))
= arcsin(0.63·1)
= 39.05°
Периметр:
P = a + b + c
= 13.65 + 10.6 + 8.6
= 32.85
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√16.43·(16.43-13.65)·(16.43-10.6)·(16.43-8.6)
=√16.43 · 2.78 · 5.83 · 7.83
=√2085.03176706
= 45.66
Высота :
ha =
2S
a
=
2 · 45.66
13.65
= 6.69
hb =
2S
b
=
2 · 45.66
10.6
= 8.615
hc =
2S
c
=
2 · 45.66
8.6
= 10.62