В треугольнике со сторонами: a = 23.5, b = 23.4, с = 42.85, углы равны α° = 24.04°, β° = 23.94°, γ° = 132°
Ответ:
a=23.5
b=23.4
c=42.85
α°=24.04°
β°=23.94°
γ°=132°
S = 204.55
ha=17.41
hb=17.48
hc=9.547
P = 89.75
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √23.52 + 23.42 - 2·23.5·23.4·cos(132°)
= √552.25 + 547.56 - 1099.8·-0.6691
= √1835.7
= 42.85
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
23.5
42.85
sin(132°))
= arcsin(0.5484·0.7431)
= 24.05°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
23.42+42.852-23.52
2·23.4·42.85
)
= arccos(
547.56+1836.1225-552.25
2005.4
)
= 24.04°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
23.4
42.85
sin(132°))
= arcsin(0.5461·0.7431)
= 23.94°
Периметр:
P = a + b + c
= 23.5 + 23.4 + 42.85
= 89.75
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√44.88·(44.88-23.5)·(44.88-23.4)·(44.88-42.85)
=√44.88 · 21.38 · 21.48 · 2.03
=√41839.92179136
= 204.55
Высота :
ha =
2S
a
=
2 · 204.55
23.5
= 17.41
hb =
2S
b
=
2 · 204.55
23.4
= 17.48
hc =
2S
c
=
2 · 204.55
42.85
= 9.547