В треугольнике со сторонами: a = 69.41, b = 50.83, с = 62.25, углы равны α° = 75°, β° = 45°, γ° = 60°
Ответ:
a=69.41
b=50.83
c=62.25
α°=75°
β°=45°
γ°=60°
S = 1528.4
ha=60
hb=60.14
hc=49.11
P = 182.49
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 62.25·
sin(45°)
sin(60°)
= 62.25·
0.7071
0.866
= 62.25·0.8165
= 50.83
Угол:
α° = 180 - γ° - β°
= 180 - 60° - 45°
= 75°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √50.832 + 62.252 - 2·50.83·62.25·cos(75°)
= √2583.7 + 3875.1 - 6328.3·0.2588
= √4821
= 69.43
или:
a = b·
sin(α°)
sin(β°)
= 50.83·
sin(75°)
sin(45°)
= 50.83·
0.9659
0.7071
= 50.83·1.366
= 69.43
или:
a = c·
sin(α°)
sin(γ°)
= 62.25·
sin(75°)
sin(60°)
= 62.25·
0.9659
0.866
= 62.25·1.115
= 69.41
Периметр:
P = a + b + c
= 69.41 + 50.83 + 62.25
= 182.49
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√91.25·(91.25-69.41)·(91.25-50.83)·(91.25-62.25)
=√91.25 · 21.84 · 40.42 · 29
=√2336037.522
= 1528.4
hb =
2S
b
=
2 · 1528.4
50.83
= 60.14
hc =
2S
c
=
2 · 1528.4
62.25
= 49.11