В треугольнике со сторонами: a = 11.15, b = 8.165, с = 10, углы равны α° = 75°, β° = 45°, γ° = 60°
Ответ:
a=11.15
b=8.165
c=10
α°=75°
β°=45°
γ°=60°
S = 39.46
ha=7.078
hb=9.666
hc=7.892
P = 29.32
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 10·
sin(45°)
sin(60°)
= 10·
0.7071
0.866
= 10·0.8165
= 8.165
Угол:
α° = 180 - γ° - β°
= 180 - 60° - 45°
= 75°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √8.1652 + 102 - 2·8.165·10·cos(75°)
= √66.67 + 100 - 163.3·0.2588
= √124.41
= 11.15
или:
a = b·
sin(α°)
sin(β°)
= 8.165·
sin(75°)
sin(45°)
= 8.165·
0.9659
0.7071
= 8.165·1.366
= 11.15
или:
a = c·
sin(α°)
sin(γ°)
= 10·
sin(75°)
sin(60°)
= 10·
0.9659
0.866
= 10·1.115
= 11.15
Периметр:
P = a + b + c
= 11.15 + 8.165 + 10
= 29.32
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√14.66·(14.66-11.15)·(14.66-8.165)·(14.66-10)
=√14.66 · 3.51 · 6.495 · 4.66
=√1557.42147522
= 39.46
Высота :
ha =
2S
a
=
2 · 39.46
11.15
= 7.078
hb =
2S
b
=
2 · 39.46
8.165
= 9.666
hc =
2S
c
=
2 · 39.46
10
= 7.892