В треугольнике со сторонами: a = 9, b = 10, с = 9.354, углы равны α° = 55.3°, β° = 66°, γ° = 58.7°
Ответ:
a=9
b=10
c=9.354
α°=55.3°
β°=66°
γ°=58.7°
S = 38.49
ha=8.553
hb=7.698
hc=8.222
P = 28.35
Решение:
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
9
10
sin(66°))
= arcsin(0.9·0.9135)
= 55.3°
Высота :
hc = a·sin(β°)
= 9·sin(66°)
= 9·0.9135
= 8.222
Угол:
γ° = 180 - α° - β°
= 180 - 55.3° - 66°
= 58.7°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √92 + 102 - 2·9·10·cos(58.7°)
= √81 + 100 - 180·0.5195
= √87.49
= 9.354
или:
c = a·
sin(γ°)
sin(α°)
= 9·
sin(58.7°)
sin(55.3°)
= 9·
0.8545
0.8221
= 9·1.039
= 9.351
или:
c = b·
sin(γ°)
sin(β°)
= 10·
sin(58.7°)
sin(66°)
= 10·
0.8545
0.9135
= 10·0.9354
= 9.354
Периметр:
P = a + b + c
= 9 + 10 + 9.354
= 28.35
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√14.18·(14.18-9)·(14.18-10)·(14.18-9.354)
=√14.18 · 5.18 · 4.18 · 4.826
=√1481.731760432
= 38.49
Высота :
ha =
2S
a
=
2 · 38.49
9
= 8.553
hb =
2S
b
=
2 · 38.49
10
= 7.698