В треугольнике со сторонами: a = 35, b = 31.82, с = 49.32, углы равны α° = 45°, β° = 40°, γ° = 95°
Ответ:
a=35
b=31.82
c=49.32
α°=45°
β°=40°
γ°=95°
S = 554.71
ha=31.7
hb=34.87
hc=22.5
P = 116.14
Решение:
Сторона:
b = a·
sin(β°)
sin(α°)
= 35·
sin(40°)
sin(45°)
= 35·
0.6428
0.7071
= 35·0.9091
= 31.82
Угол:
γ° = 180 - α° - β°
= 180 - 45° - 40°
= 95°
Высота :
hc = a·sin(β°)
= 35·sin(40°)
= 35·0.6428
= 22.5
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √352 + 31.822 - 2·35·31.82·cos(95°)
= √1225 + 1012.5 - 2227.4·-0.08716
= √2431.6
= 49.31
или:
c = a·
sin(γ°)
sin(α°)
= 35·
sin(95°)
sin(45°)
= 35·
0.9962
0.7071
= 35·1.409
= 49.32
или:
c = b·
sin(γ°)
sin(β°)
= 31.82·
sin(95°)
sin(40°)
= 31.82·
0.9962
0.6428
= 31.82·1.55
= 49.32
Периметр:
P = a + b + c
= 35 + 31.82 + 49.32
= 116.14
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√58.07·(58.07-35)·(58.07-31.82)·(58.07-49.32)
=√58.07 · 23.07 · 26.25 · 8.75
=√307706.57859375
= 554.71
Высота :
ha =
2S
a
=
2 · 554.71
35
= 31.7
hb =
2S
b
=
2 · 554.71
31.82
= 34.87