В треугольнике со сторонами: a = 11.39, b = 4.044, с = 10, углы равны α° = 99.5°, β° = 20.5°, γ° = 60°
Ответ:
a=11.39
b=4.044
c=10
α°=99.5°
β°=20.5°
γ°=60°
S = 19.98
ha=4
hb=9.881
hc=3.996
P = 25.43
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 10·
sin(20.5°)
sin(60°)
= 10·
0.3502
0.866
= 10·0.4044
= 4.044
Угол:
α° = 180 - γ° - β°
= 180 - 60° - 20.5°
= 99.5°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √4.0442 + 102 - 2·4.044·10·cos(99.5°)
= √16.35 + 100 - 80.88·-0.165
= √129.7
= 11.39
или:
a = b·
sin(α°)
sin(β°)
= 4.044·
sin(99.5°)
sin(20.5°)
= 4.044·
0.9863
0.3502
= 4.044·2.816
= 11.39
или:
a = c·
sin(α°)
sin(γ°)
= 10·
sin(99.5°)
sin(60°)
= 10·
0.9863
0.866
= 10·1.139
= 11.39
Периметр:
P = a + b + c
= 11.39 + 4.044 + 10
= 25.43
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√12.72·(12.72-11.39)·(12.72-4.044)·(12.72-10)
=√12.72 · 1.33 · 8.676 · 2.72
=√399.233705472
= 19.98
hb =
2S
b
=
2 · 19.98
4.044
= 9.881
hc =
2S
c
=
2 · 19.98
10
= 3.996