В треугольнике со сторонами: a = 102.14, b = 64.2, с = 98.87, углы равны α° = 74.2°, β° = 37.2°, γ° = 68.6°
Ответ:
a=102.14
b=64.2
c=98.87
α°=74.2°
β°=37.2°
γ°=68.6°
S = 3053.9
ha=40
hb=95.14
hc=61.78
P = 265.21
Решение:
Угол:
β° = 180 - γ° - α°
= 180 - 68.6° - 74.2°
= 37.2°
Сторона:
a = b·
sin(α°)
sin(β°)
= 64.2·
sin(74.2°)
sin(37.2°)
= 64.2·
0.9622
0.6046
= 64.2·1.591
= 102.14
Сторона:
c = b·
sin(γ°)
sin(β°)
= 64.2·
sin(68.6°)
sin(37.2°)
= 64.2·
0.9311
0.6046
= 64.2·1.54
= 98.87
Периметр:
P = a + b + c
= 102.14 + 64.2 + 98.87
= 265.21
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√132.61·(132.61-102.14)·(132.61-64.2)·(132.61-98.87)
=√132.61 · 30.47 · 68.41 · 33.74
=√9326386.2557358
= 3053.9
hb =
2S
b
=
2 · 3053.9
64.2
= 95.14
hc =
2S
c
=
2 · 3053.9
98.87
= 61.78