В треугольнике со сторонами: a = 500, b = 500, с = 999.95 высоты равны ha = 10.95, hb = 10.95, hc = 5.477
Ответ:
a=500
b=500
c=999.95
α°=0.573°
β°=0.4999°
γ°=179°
S = 2738.5
ha=10.95
hb=10.95
hc=5.477
P = 2000
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5002 + 5002 - 2·500·500·cos(179°)
= √250000 + 250000 - 500000·-0.9998
= √999900
= 999.95
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
500
999.95
sin(179°))
= arcsin(0.5·0.01745)
= 0.4999°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5002+999.952-5002
2·500·999.95
)
= arccos(
250000+999900.0025-250000
999950
)
= 0.573°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
500
999.95
sin(179°))
= arcsin(0.5·0.01745)
= 0.4999°
Периметр:
P = a + b + c
= 500 + 500 + 999.95
= 2000
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√999.98·(999.98-500)·(999.98-500)·(999.98-999.95)
=√999.98 · 499.98 · 499.98 · 0.029999999999973
=√7499250.0239929
= 2738.5
Высота :
ha =
2S
a
=
2 · 2738.5
500
= 10.95
hb =
2S
b
=
2 · 2738.5
500
= 10.95
hc =
2S
c
=
2 · 2738.5
999.95
= 5.477