В треугольнике со сторонами: a = 457.19, b = 349.8, с = 457.19, углы равны α° = 67.5°, β° = 45°, γ° = 67.5°
Ответ:
a=457.19
b=349.8
c=457.19
α°=67.5°
β°=45°
γ°=67.5°
S = 73880
ha=323.1
hb=422.41
hc=323.28
P = 1264.2
Решение:
Сторона:
a = b·
sin(α°)
sin(β°)
= 349.8·
sin(67.5°)
sin(45°)
= 349.8·
0.9239
0.7071
= 349.8·1.307
= 457.19
Угол:
γ° = 180 - α° - β°
= 180 - 67.5° - 45°
= 67.5°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √457.192 + 349.82 - 2·457.19·349.8·cos(67.5°)
= √209022.7 + 122360 - 319850.1·0.3827
= √208976.1
= 457.14
или:
c = a·
sin(γ°)
sin(α°)
= 457.19·
sin(67.5°)
sin(67.5°)
= 457.19·
0.9239
0.9239
= 457.19·1
= 457.19
или:
c = b·
sin(γ°)
sin(β°)
= 349.8·
sin(67.5°)
sin(45°)
= 349.8·
0.9239
0.7071
= 349.8·1.307
= 457.19
Высота :
hc = a·sin(β°)
= 457.19·sin(45°)
= 457.19·0.7071
= 323.28
Периметр:
P = a + b + c
= 457.19 + 349.8 + 457.19
= 1264.2
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√632.09·(632.09-457.19)·(632.09-349.8)·(632.09-457.19)
=√632.09 · 174.9 · 282.29 · 174.9
=√5458257652.1259
= 73880
hb =
2S
b
=
2 · 73880
349.8
= 422.41