В треугольнике со сторонами: a = 4.86, b = 9, с = 6.457, углы равны α° = 31.53°, β° = 104.47°, γ° = 44°
Ответ:
a=4.86
b=9
c=6.457
α°=31.53°
β°=104.47°
γ°=44°
S = 15.21
ha=6.259
hb=3.38
hc=4.711
P = 20.32
Решение:
Сторона:
c = b·
sin(γ°)
sin(β°)
= 9·
sin(44°)
sin(104.47°)
= 9·
0.6947
0.9683
= 9·0.7174
= 6.457
Угол:
α° = 180 - γ° - β°
= 180 - 44° - 104.47°
= 31.53°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √92 + 6.4572 - 2·9·6.457·cos(31.53°)
= √81 + 41.69 - 116.23·0.8524
= √23.62
= 4.86
или:
a = b·
sin(α°)
sin(β°)
= 9·
sin(31.53°)
sin(104.47°)
= 9·
0.5229
0.9683
= 9·0.54
= 4.86
или:
a = c·
sin(α°)
sin(γ°)
= 6.457·
sin(31.53°)
sin(44°)
= 6.457·
0.5229
0.6947
= 6.457·0.7527
= 4.86
Периметр:
P = a + b + c
= 4.86 + 9 + 6.457
= 20.32
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√10.16·(10.16-4.86)·(10.16-9)·(10.16-6.457)
=√10.16 · 5.3 · 1.16 · 3.703
=√231.30300704
= 15.21
Высота :
ha =
2S
a
=
2 · 15.21
4.86
= 6.259
hb =
2S
b
=
2 · 15.21
9
= 3.38
hc =
2S
c
=
2 · 15.21
6.457
= 4.711