В треугольнике со сторонами: a = 3.138, b = 2.45, с = 3.45, углы равны α° = 61.54°, β° = 43.35°, γ° = 75.07°
Ответ:
a=3.138
b=2.45
c=3.45
α°=61.54°
β°=43.35°
γ°=75.07°
S = 3.715
ha=2.368
hb=3.033
hc=2.154
P = 9.038
Решение:
Угол:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
2.452+3.452-3.1382
2·2.45·3.45
)
= arccos(
6.0025+11.9025-9.847044
16.91
)
= 61.54°
Периметр:
P = a + b + c
= 3.138 + 2.45 + 3.45
= 9.038
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√4.519·(4.519-3.138)·(4.519-2.45)·(4.519-3.45)
=√4.519 · 1.381 · 2.069 · 1.069
=√13.803023131379
= 3.715
Высота :
ha =
2S
a
=
2 · 3.715
3.138
= 2.368
hb =
2S
b
=
2 · 3.715
2.45
= 3.033
hc =
2S
c
=
2 · 3.715
3.45
= 2.154
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
2.45
3.138
sin(61.54°))
= arcsin(0.7808·0.8792)
= 43.35°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
3.45
3.138
sin(61.54°))
= arcsin(1.099·0.8792)
= 75.07°