В треугольнике со сторонами: a = 4.62, b = 4.06, с = 3, углы равны α° = 80.22°, β° = 60°, γ° = 39.78°
Ответ:
a=4.62
b=4.06
c=3
α°=80.22°
β°=60°
γ°=39.78°
S = 6.001
ha=4
hb=2.956
hc=4.001
P = 11.68
Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √4.622 + 32 - 2·4.62·3·cos(60°)
= √21.34 + 9 - 27.72·0.5
= √16.48
= 4.06
Высота :
hc = a·sin(β°)
= 4.62·sin(60°)
= 4.62·0.866
= 4.001
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
4.62
4.06
sin(60°))
= arcsin(1.138·0.866)
= 80.23°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
4.062+32-4.622
2·4.06·3
)
= arccos(
16.4836+9-21.3444
24.36
)
= 80.22°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
3
4.06
sin(60°))
= arcsin(0.7389·0.866)
= 39.78°
Периметр:
P = a + b + c
= 4.62 + 4.06 + 3
= 11.68
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.84·(5.84-4.62)·(5.84-4.06)·(5.84-3)
=√5.84 · 1.22 · 1.78 · 2.84
=√36.01728896
= 6.001
hb =
2S
b
=
2 · 6.001
4.06
= 2.956