В треугольнике со сторонами: a = 1.406, b = 2, с = 2.014, углы равны α° = 41°, β° = 69°, γ° = 70°
Ответ:
a=1.406
b=2
c=2.014
α°=41°
β°=69°
γ°=70°
S = 1.321
ha=1.879
hb=1.321
hc=1.312
P = 5.42
Решение:
Сторона:
c = b·
sin(γ°)
sin(β°)
= 2·
sin(70°)
sin(69°)
= 2·
0.9397
0.9336
= 2·1.007
= 2.014
Угол:
α° = 180 - γ° - β°
= 180 - 70° - 69°
= 41°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √22 + 2.0142 - 2·2·2.014·cos(41°)
= √4 + 4.056 - 8.056·0.7547
= √1.976
= 1.406
или:
a = b·
sin(α°)
sin(β°)
= 2·
sin(41°)
sin(69°)
= 2·
0.6561
0.9336
= 2·0.7028
= 1.406
или:
a = c·
sin(α°)
sin(γ°)
= 2.014·
sin(41°)
sin(70°)
= 2.014·
0.6561
0.9397
= 2.014·0.6982
= 1.406
Периметр:
P = a + b + c
= 1.406 + 2 + 2.014
= 5.42
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√2.71·(2.71-1.406)·(2.71-2)·(2.71-2.014)
=√2.71 · 1.304 · 0.71 · 0.696
=√1.7462823744
= 1.321
Высота :
ha =
2S
a
=
2 · 1.321
1.406
= 1.879
hb =
2S
b
=
2 · 1.321
2
= 1.321
hc =
2S
c
=
2 · 1.321
2.014
= 1.312