В треугольнике со сторонами: a = 11, b = 10, с = 5.999, углы равны α° = 82.82°, β° = 64.42°, γ° = 32.76°
Ответ:
a=11
b=10
c=5.999
α°=82.82°
β°=64.42°
γ°=32.76°
S = 29.77
ha=5.413
hb=5.954
hc=9.922
P = 27
Решение:
Угол:
α° = 180 - γ° - β°
= 180 - 32.76° - 64.42°
= 82.82°
Высота :
hc = a·sin(β°)
= 11·sin(64.42°)
= 11·0.902
= 9.922
Сторона:
b = a·
sin(β°)
sin(α°)
= 11·
sin(64.42°)
sin(82.82°)
= 11·
0.902
0.9922
= 11·0.9091
= 10
Сторона:
c = a·
sin(γ°)
sin(α°)
= 11·
sin(32.76°)
sin(82.82°)
= 11·
0.5411
0.9922
= 11·0.5454
= 5.999
Периметр:
P = a + b + c
= 11 + 10 + 5.999
= 27
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√13.5·(13.5-11)·(13.5-10)·(13.5-5.999)
=√13.5 · 2.5 · 3.5 · 7.501
=√886.055625
= 29.77
Высота :
ha =
2S
a
=
2 · 29.77
11
= 5.413
hb =
2S
b
=
2 · 29.77
10
= 5.954