В треугольнике со сторонами: a = 50, b = 65, с = 82.01, углы равны α° = 37.57°, β° = 52.43°, γ° = 90°
Ответ:
a=50
b=65
c=82.01
α°=37.57°
β°=52.43°
γ°=90°
S = 1625.5
ha=65.02
hb=50.02
hc=39.64
P = 197.01
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √502 + 652 - 2·50·65·cos(90°)
= √2500 + 4225 - 6500·0
= √6725
= 82.01
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
50
82.01
sin(90°))
= arcsin(0.6097·1)
= 37.57°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
652+82.012-502
2·65·82.01
)
= arccos(
4225+6725.6401-2500
10661.3
)
= 37.57°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
65
82.01
sin(90°))
= arcsin(0.7926·1)
= 52.43°
Периметр:
P = a + b + c
= 50 + 65 + 82.01
= 197.01
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√98.51·(98.51-50)·(98.51-65)·(98.51-82.01)
=√98.51 · 48.51 · 33.51 · 16.5
=√2642226.0240915
= 1625.5
Высота :
ha =
2S
a
=
2 · 1625.5
50
= 65.02
hb =
2S
b
=
2 · 1625.5
65
= 50.02
hc =
2S
c
=
2 · 1625.5
82.01
= 39.64