В треугольнике со сторонами: a = 142.36, b = 173.1, с = 100, углы равны α° = 55.33°, β° = 90°, γ° = 35.29°
Ответ:
a=142.36
b=173.1
c=100
α°=55.33°
β°=90°
γ°=35.29°
S = 7117.6
ha=99.99
hb=82.24
hc=142.35
P = 415.46
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √173.12 + 1002 - 2·173.1·100·cos(55.33°)
= √29963.6 + 10000 - 34620·0.5688
= √20271.7
= 142.38
или:
a = b·
sin(α°)
sin(β°)
= 173.1·
sin(55.33°)
sin(90°)
= 173.1·
0.8224
1
= 173.1·0.8224
= 142.36
Угол:
γ° = 180 - α° - β°
= 180 - 55.33° - 90°
= 34.67°
или:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
100
173.1
sin(90°))
= arcsin(0.5777·1)
= 35.29°
Периметр:
P = a + b + c
= 142.36 + 173.1 + 100
= 415.46
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√207.73·(207.73-142.36)·(207.73-173.1)·(207.73-100)
=√207.73 · 65.37 · 34.63 · 107.73
=√50660195.039038
= 7117.6
Высота :
ha =
2S
a
=
2 · 7117.6
142.36
= 99.99
hb =
2S
b
=
2 · 7117.6
173.1
= 82.24
hc =
2S
c
=
2 · 7117.6
100
= 142.35