В треугольнике со сторонами: a = 52, b = 47, с = 42.08 высоты равны ha = 36, hb = 39.83, hc = 44.49
Ответ:
a=52
b=47
c=42.08
α°=71.18°
β°=58.83°
γ°=50°
S = 936.04
ha=36
hb=39.83
hc=44.49
P = 141.08
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √522 + 472 - 2·52·47·cos(50°)
= √2704 + 2209 - 4888·0.6428
= √1771
= 42.08
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
52
42.08
sin(50°))
= arcsin(1.236·0.766)
= 71.22°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
472+42.082-522
2·47·42.08
)
= arccos(
2209+1770.7264-2704
3955.5
)
= 71.18°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
47
42.08
sin(50°))
= arcsin(1.117·0.766)
= 58.83°
Периметр:
P = a + b + c
= 52 + 47 + 42.08
= 141.08
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√70.54·(70.54-52)·(70.54-47)·(70.54-42.08)
=√70.54 · 18.54 · 23.54 · 28.46
=√876166.28892144
= 936.04
Высота :
ha =
2S
a
=
2 · 936.04
52
= 36
hb =
2S
b
=
2 · 936.04
47
= 39.83
hc =
2S
c
=
2 · 936.04
42.08
= 44.49