В треугольнике со сторонами: a = 0.16, b = 0.8, с = 0.868, углы равны α° = 9.974°, β° = 60°, γ° = 110.026°
Ответ:
a=0.16
b=0.8
c=0.868
α°=9.974°
β°=60°
γ°=110.026°
S = 0.06012
ha=0.7515
hb=0.1503
hc=0.1386
P = 1.828
Решение:
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
0.16
0.8
sin(60°))
= arcsin(0.2·0.866)
= 9.974°
Высота :
hc = a·sin(β°)
= 0.16·sin(60°)
= 0.16·0.866
= 0.1386
Угол:
γ° = 180 - α° - β°
= 180 - 9.974° - 60°
= 110.026°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √0.162 + 0.82 - 2·0.16·0.8·cos(110.026°)
= √0.0256 + 0.64 - 0.256·-0.3424
= √0.7533
= 0.8679
или:
c = a·
sin(γ°)
sin(α°)
= 0.16·
sin(110.026°)
sin(9.974°)
= 0.16·
0.9395
0.1732
= 0.16·5.424
= 0.8678
или:
c = b·
sin(γ°)
sin(β°)
= 0.8·
sin(110.026°)
sin(60°)
= 0.8·
0.9395
0.866
= 0.8·1.085
= 0.868
Периметр:
P = a + b + c
= 0.16 + 0.8 + 0.868
= 1.828
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√0.914·(0.914-0.16)·(0.914-0.8)·(0.914-0.868)
=√0.914 · 0.754 · 0.114 · 0.046
=√0.003613934064
= 0.06012
Высота :
ha =
2S
a
=
2 · 0.06012
0.16
= 0.7515
hb =
2S
b
=
2 · 0.06012
0.8
= 0.1503