В треугольнике со сторонами: a = 13, b = 11, с = 16, углы равны α° = 53.77°, β° = 43.06°, γ° = 83.17°
Ответ:
a=13
b=11
c=16
α°=53.77°
β°=43.06°
γ°=83.17°
S = 70.99
ha=10.92
hb=12.91
hc=8.874
P = 40
Решение:
Сторона:
b = c·
sin(β°)
sin(γ°)
= 16·
sin(43.06°)
sin(83.17°)
= 16·
0.6828
0.9929
= 16·0.6877
= 11
Угол:
α° = 180 - γ° - β°
= 180 - 83.17° - 43.06°
= 53.77°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √112 + 162 - 2·11·16·cos(53.77°)
= √121 + 256 - 352·0.591
= √168.97
= 13
или:
a = b·
sin(α°)
sin(β°)
= 11·
sin(53.77°)
sin(43.06°)
= 11·
0.8067
0.6828
= 11·1.181
= 12.99
или:
a = c·
sin(α°)
sin(γ°)
= 16·
sin(53.77°)
sin(83.17°)
= 16·
0.8067
0.9929
= 16·0.8125
= 13
Периметр:
P = a + b + c
= 13 + 11 + 16
= 40
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√20·(20-13)·(20-11)·(20-16)
=√20 · 7 · 9 · 4
=√5040
= 70.99
Высота :
ha =
2S
a
=
2 · 70.99
13
= 10.92
hb =
2S
b
=
2 · 70.99
11
= 12.91
hc =
2S
c
=
2 · 70.99
16
= 8.874