В треугольнике со сторонами: a = 1.414, b = 2.236, с = 3, углы равны α° = 26.56°, β° = 45°, γ° = 108.44°
Ответ:
a=1.414
b=2.236
c=3
α°=26.56°
β°=45°
γ°=108.44°
S = 1.5
ha=1
hb=1.342
hc=1
P = 6.65
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 3·
sin(45°)
sin(108.44°)
= 3·
0.7071
0.9487
= 3·0.7453
= 2.236
Угол:
α° = 180 - γ° - β°
= 180 - 108.44° - 45°
= 26.56°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √2.2362 + 32 - 2·2.236·3·cos(26.56°)
= √5 + 9 - 13.42·0.8945
= √1.996
= 1.413
или:
a = b·
sin(α°)
sin(β°)
= 2.236·
sin(26.56°)
sin(45°)
= 2.236·
0.4471
0.7071
= 2.236·0.6323
= 1.414
или:
a = c·
sin(α°)
sin(γ°)
= 3·
sin(26.56°)
sin(108.44°)
= 3·
0.4471
0.9487
= 3·0.4713
= 1.414
Периметр:
P = a + b + c
= 1.414 + 2.236 + 3
= 6.65
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.325·(3.325-1.414)·(3.325-2.236)·(3.325-3)
=√3.325 · 1.911 · 1.089 · 0.325
=√2.248865994375
= 1.5
hb =
2S
b
=
2 · 1.5
2.236
= 1.342
hc =
2S
c
=
2 · 1.5
3
= 1