В треугольнике со сторонами: a = 5, b = 3, с = 2.158, углы равны α° = 151.15°, β° = 16.8°, γ° = 12°
Ответ:
a=5
b=3
c=2.158
α°=151.15°
β°=16.8°
γ°=12°
S = 1.561
ha=0.6244
hb=1.041
hc=1.447
P = 10.16
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √52 + 32 - 2·5·3·cos(12°)
= √25 + 9 - 30·0.9781
= √4.657
= 2.158
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5
2.158
sin(12°))
= arcsin(2.317·0.2079)
= 28.8°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
32+2.1582-52
2·3·2.158
)
= arccos(
9+4.656964-25
12.95
)
= 151.15°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
3
2.158
sin(12°))
= arcsin(1.39·0.2079)
= 16.8°
Периметр:
P = a + b + c
= 5 + 3 + 2.158
= 10.16
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.079·(5.079-5)·(5.079-3)·(5.079-2.158)
=√5.079 · 0.079 · 2.079 · 2.921
=√2.436639893919
= 1.561
Высота :
ha =
2S
a
=
2 · 1.561
5
= 0.6244
hb =
2S
b
=
2 · 1.561
3
= 1.041
hc =
2S
c
=
2 · 1.561
2.158
= 1.447