В треугольнике со сторонами: a = 625.87, b = 499.5, с = 499.5, углы равны α° = 77.6°, β° = 51.2°, γ° = 51.2°
Ответ:
a=625.87
b=499.5
c=499.5
α°=77.6°
β°=51.2°
γ°=51.2°
S = 121836.6
ha=389.34
hb=487.83
hc=487.83
P = 1624.9
Решение:
Угол:
α° = 180 - γ° - β°
= 180 - 51.2° - 51.2°
= 77.6°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √499.52 + 499.52 - 2·499.5·499.5·cos(77.6°)
= √249500.3 + 249500.3 - 499000.5·0.2147
= √391865.2
= 625.99
или:
a = b·
sin(α°)
sin(β°)
= 499.5·
sin(77.6°)
sin(51.2°)
= 499.5·
0.9767
0.7793
= 499.5·1.253
= 625.87
или:
a = c·
sin(α°)
sin(γ°)
= 499.5·
sin(77.6°)
sin(51.2°)
= 499.5·
0.9767
0.7793
= 499.5·1.253
= 625.87
Периметр:
P = a + b + c
= 625.87 + 499.5 + 499.5
= 1624.9
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√812.44·(812.44-625.87)·(812.44-499.5)·(812.44-499.5)
=√812.44 · 186.57 · 312.94 · 312.94
=√14844147649.701
= 121836.6
Высота :
ha =
2S
a
=
2 · 121836.6
625.87
= 389.34
hb =
2S
b
=
2 · 121836.6
499.5
= 487.83
hc =
2S
c
=
2 · 121836.6
499.5
= 487.83