В треугольнике со сторонами: a = 164, b = 103.84, с = 103.81, углы равны α° = 104.33°, β° = 37.84°, γ° = 37.83°
Ответ:
a=164
b=103.84
c=103.81
α°=104.33°
β°=37.84°
γ°=37.83°
S = 5223.1
ha=63.7
hb=100.6
hc=100.61
P = 371.65
Решение:
Сторона:
b = a·
sin(β°)
sin(α°)
= 164·
sin(37.84°)
sin(104.33°)
= 164·
0.6135
0.9689
= 164·0.6332
= 103.84
Угол:
γ° = 180 - α° - β°
= 180 - 104.33° - 37.84°
= 37.83°
Высота :
hc = a·sin(β°)
= 164·sin(37.84°)
= 164·0.6135
= 100.61
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √1642 + 103.842 - 2·164·103.84·cos(37.83°)
= √26896 + 10782.7 - 34059.5·0.7898
= √10778.5
= 103.82
или:
c = a·
sin(γ°)
sin(α°)
= 164·
sin(37.83°)
sin(104.33°)
= 164·
0.6133
0.9689
= 164·0.633
= 103.81
или:
c = b·
sin(γ°)
sin(β°)
= 103.84·
sin(37.83°)
sin(37.84°)
= 103.84·
0.6133
0.6135
= 103.84·0.9997
= 103.81
Периметр:
P = a + b + c
= 164 + 103.84 + 103.81
= 371.65
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√185.83·(185.83-164)·(185.83-103.84)·(185.83-103.81)
=√185.83 · 21.83 · 81.99 · 82.02
=√27280367.340764
= 5223.1
Высота :
ha =
2S
a
=
2 · 5223.1
164
= 63.7
hb =
2S
b
=
2 · 5223.1
103.84
= 100.6