В треугольнике со сторонами: a = 13.5, b = 27, с = 23.38, углы равны α° = 30°, β° = 90°, γ° = 60°
Ответ:
a=13.5
b=27
c=23.38
α°=30°
β°=90°
γ°=60°
S = 157.81
ha=23.38
hb=11.69
hc=13.5
P = 63.88
Решение:
Сторона:
c = b·
sin(γ°)
sin(β°)
= 27·
sin(60°)
sin(90°)
= 27·
0.866
1
= 27·0.866
= 23.38
Угол:
α° = 180 - γ° - β°
= 180 - 60° - 90°
= 30°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √272 + 23.382 - 2·27·23.38·cos(30°)
= √729 + 546.62 - 1262.5·0.866
= √182.3
= 13.5
или:
a = b·
sin(α°)
sin(β°)
= 27·
sin(30°)
sin(90°)
= 27·
0.5
1
= 27·0.5
= 13.5
или:
a = c·
sin(α°)
sin(γ°)
= 23.38·
sin(30°)
sin(60°)
= 23.38·
0.5
0.866
= 23.38·0.5774
= 13.5
Периметр:
P = a + b + c
= 13.5 + 27 + 23.38
= 63.88
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√31.94·(31.94-13.5)·(31.94-27)·(31.94-23.38)
=√31.94 · 18.44 · 4.94 · 8.56
=√24905.57323904
= 157.81
Высота :
ha =
2S
a
=
2 · 157.81
13.5
= 23.38
hb =
2S
b
=
2 · 157.81
27
= 11.69
hc =
2S
c
=
2 · 157.81
23.38
= 13.5