В треугольнике со сторонами: a = 82.27, b = 49.2, с = 95, углы равны α° = 60°, β° = 30°, γ° = 90°
Ответ:
a=82.27
b=49.2
c=95
α°=60°
β°=30°
γ°=90°
S = 2024
ha=49.2
hb=82.28
hc=42.61
P = 226.47
Решение:
Угол:
α° = 180 - γ° - β°
= 180 - 90° - 30°
= 60°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √49.22 + 952 - 2·49.2·95·cos(60°)
= √2420.6 + 9025 - 9348·0.5
= √6771.6
= 82.29
или:
a = b·
sin(α°)
sin(β°)
= 49.2·
sin(60°)
sin(30°)
= 49.2·
0.866
0.5
= 49.2·1.732
= 85.21
или:
a = c·
sin(α°)
sin(γ°)
= 95·
sin(60°)
sin(90°)
= 95·
0.866
1
= 95·0.866
= 82.27
Периметр:
P = a + b + c
= 82.27 + 49.2 + 95
= 226.47
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√113.24·(113.24-82.27)·(113.24-49.2)·(113.24-95)
=√113.24 · 30.97 · 64.04 · 18.24
=√4096540.2214349
= 2024
Высота :
ha =
2S
a
=
2 · 2024
82.27
= 49.2
hb =
2S
b
=
2 · 2024
49.2
= 82.28
hc =
2S
c
=
2 · 2024
95
= 42.61