В треугольнике со сторонами: a = 99.45, b = 99.45, с = 19.08 высоты равны ha = 18.99, hb = 18.99, hc = 98.99
Ответ:
a=99.45
b=99.45
c=19.08
α°=84.5°
β°=83.96°
γ°=11°
S = 944.38
ha=18.99
hb=18.99
hc=98.99
P = 217.98
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √99.452 + 99.452 - 2·99.45·99.45·cos(11°)
= √9890.3 + 9890.3 - 19780.6·0.9816
= √363.96
= 19.08
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
99.45
19.08
sin(11°))
= arcsin(5.212·0.1908)
= 83.96°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
99.452+19.082-99.452
2·99.45·19.08
)
= arccos(
9890.3025+364.0464-9890.3025
3795
)
= 84.5°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
99.45
19.08
sin(11°))
= arcsin(5.212·0.1908)
= 83.96°
Периметр:
P = a + b + c
= 99.45 + 99.45 + 19.08
= 217.98
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√108.99·(108.99-99.45)·(108.99-99.45)·(108.99-19.08)
=√108.99 · 9.54 · 9.54 · 89.91
=√891849.14367444
= 944.38
Высота :
ha =
2S
a
=
2 · 944.38
99.45
= 18.99
hb =
2S
b
=
2 · 944.38
99.45
= 18.99
hc =
2S
c
=
2 · 944.38
19.08
= 98.99