В треугольнике со сторонами: a = 20.6, b = 23.8, с = 34.32, углы равны α° = 36.1°, β° = 42.9°, γ° = 101°
Ответ:
a=20.6
b=23.8
c=34.32
α°=36.1°
β°=42.9°
γ°=101°
S = 240.64
ha=23.36
hb=20.22
hc=14.02
P = 78.72
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √20.62 + 23.82 - 2·20.6·23.8·cos(101°)
= √424.36 + 566.44 - 980.56·-0.1908
= √1177.9
= 34.32
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
20.6
34.32
sin(101°))
= arcsin(0.6002·0.9816)
= 36.1°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
23.82+34.322-20.62
2·23.8·34.32
)
= arccos(
566.44+1177.8624-424.36
1633.6
)
= 36.1°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
23.8
34.32
sin(101°))
= arcsin(0.6935·0.9816)
= 42.9°
Периметр:
P = a + b + c
= 20.6 + 23.8 + 34.32
= 78.72
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√39.36·(39.36-20.6)·(39.36-23.8)·(39.36-34.32)
=√39.36 · 18.76 · 15.56 · 5.04
=√57906.59825664
= 240.64
Высота :
ha =
2S
a
=
2 · 240.64
20.6
= 23.36
hb =
2S
b
=
2 · 240.64
23.8
= 20.22
hc =
2S
c
=
2 · 240.64
34.32
= 14.02