В треугольнике со сторонами: a = 5.3, b = 5.3, с = 1.199, углы равны α° = 83.51°, β° = 83.99°, γ° = 13°
Ответ:
a=5.3
b=5.3
c=1.199
α°=83.51°
β°=83.99°
γ°=13°
S = 3.16
ha=5
hb=1.192
hc=5.271
P = 11.8
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √5.32 + 5.32 - 2·5.3·5.3·cos(13°)
= √28.09 + 28.09 - 56.18·0.9744
= √1.438
= 1.199
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
5.3
1.199
sin(13°))
= arcsin(4.42·0.225)
= 83.99°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
5.32+1.1992-5.32
2·5.3·1.199
)
= arccos(
28.09+1.437601-28.09
12.71
)
= 83.51°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
5.3
1.199
sin(13°))
= arcsin(4.42·0.225)
= 83.99°
Периметр:
P = a + b + c
= 5.3 + 5.3 + 1.199
= 11.8
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.9·(5.9-5.3)·(5.9-5.3)·(5.9-1.199)
=√5.9 · 0.6 · 0.6 · 4.701
=√9.984924
= 3.16
hb =
2S
b
=
2 · 3.16
5.3
= 1.192
hc =
2S
c
=
2 · 3.16
1.199
= 5.271