В треугольнике со сторонами: a = 494.8, b = 550, с = 400, углы равны α° = 60.37°, β° = 75°, γ° = 44.63°
Ответ:
a=494.8
b=550
c=400
α°=60.37°
β°=75°
γ°=44.63°
S = 95596.3
ha=386.4
hb=347.62
hc=477.98
P = 1444.8
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
400
550
sin(75°))
= arcsin(0.7273·0.9659)
= 44.63°
Угол:
α° = 180 - γ° - β°
= 180 - 44.63° - 75°
= 60.37°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √5502 + 4002 - 2·550·400·cos(60.37°)
= √302500 + 160000 - 440000·0.4944
= √244964
= 494.94
или:
a = b·
sin(α°)
sin(β°)
= 550·
sin(60.37°)
sin(75°)
= 550·
0.8692
0.9659
= 550·0.8999
= 494.95
или:
a = c·
sin(α°)
sin(γ°)
= 400·
sin(60.37°)
sin(44.63°)
= 400·
0.8692
0.7025
= 400·1.237
= 494.8
Периметр:
P = a + b + c
= 494.8 + 550 + 400
= 1444.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√722.4·(722.4-494.8)·(722.4-550)·(722.4-400)
=√722.4 · 227.6 · 172.4 · 322.4
=√9138655155.3024
= 95596.3
Высота :
ha =
2S
a
=
2 · 95596.3
494.8
= 386.4
hb =
2S
b
=
2 · 95596.3
550
= 347.62
hc =
2S
c
=
2 · 95596.3
400
= 477.98