В треугольнике со сторонами: a = 13, b = 23, с = 27.39, углы равны α° = 28.21°, β° = 56.77°, γ° = 95°
Ответ:
a=13
b=23
c=27.39
α°=28.21°
β°=56.77°
γ°=95°
S = 149.09
ha=22.94
hb=12.96
hc=10.89
P = 63.39
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √132 + 232 - 2·13·23·cos(95°)
= √169 + 529 - 598·-0.08716
= √750.12
= 27.39
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
13
27.39
sin(95°))
= arcsin(0.4746·0.9962)
= 28.22°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
232+27.392-132
2·23·27.39
)
= arccos(
529+750.2121-169
1259.9
)
= 28.21°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
23
27.39
sin(95°))
= arcsin(0.8397·0.9962)
= 56.77°
Периметр:
P = a + b + c
= 13 + 23 + 27.39
= 63.39
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√31.7·(31.7-13)·(31.7-23)·(31.7-27.39)
=√31.7 · 18.7 · 8.7 · 4.31
=√22227.84663
= 149.09
Высота :
ha =
2S
a
=
2 · 149.09
13
= 22.94
hb =
2S
b
=
2 · 149.09
23
= 12.96
hc =
2S
c
=
2 · 149.09
27.39
= 10.89