В треугольнике со сторонами: a = 1207.7, b = 1500, с = 890, углы равны α° = 53.61°, β° = 90°, γ° = 36.39°
Ответ:
a=1207.7
b=1500
c=890
α°=53.61°
β°=90°
γ°=36.39°
S = 537516.4
ha=890.15
hb=716.69
hc=1207.9
P = 3597.7
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
890
1500
sin(90°))
= arcsin(0.5933·1)
= 36.39°
Угол:
α° = 180 - γ° - β°
= 180 - 36.39° - 90°
= 53.61°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √15002 + 8902 - 2·1500·890·cos(53.61°)
= √2250000 + 792100 - 2670000·0.5933
= √1457989
= 1207.5
или:
a = b·
sin(α°)
sin(β°)
= 1500·
sin(53.61°)
sin(90°)
= 1500·
0.805
1
= 1500·0.805
= 1207.5
или:
a = c·
sin(α°)
sin(γ°)
= 890·
sin(53.61°)
sin(36.39°)
= 890·
0.805
0.5933
= 890·1.357
= 1207.7
Периметр:
P = a + b + c
= 1207.7 + 1500 + 890
= 3597.7
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√1798.9·(1798.9-1207.7)·(1798.9-1500)·(1798.9-890)
=√1798.9 · 591.2 · 298.9 · 908.9
=√288923898102.63
= 537516.4
Высота :
ha =
2S
a
=
2 · 537516.4
1207.7
= 890.15
hb =
2S
b
=
2 · 537516.4
1500
= 716.69
hc =
2S
c
=
2 · 537516.4
890
= 1207.9