В треугольнике со сторонами: a = 1, b = 1, с = 1.474 высоты равны ha = 0.9962, hb = 0.9962, hc = 0.6758
Ответ:
a=1
b=1
c=1.474
α°=42.52°
β°=42.52°
γ°=95°
S = 0.4981
ha=0.9962
hb=0.9962
hc=0.6758
P = 3.474
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √12 + 12 - 2·1·1·cos(95°)
= √1 + 1 - 2·-0.08716
= √2.174
= 1.474
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
1
1.474
sin(95°))
= arcsin(0.6784·0.9962)
= 42.52°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
12+1.4742-12
2·1·1.474
)
= arccos(
1+2.172676-1
2.948
)
= 42.52°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
1
1.474
sin(95°))
= arcsin(0.6784·0.9962)
= 42.52°
Периметр:
P = a + b + c
= 1 + 1 + 1.474
= 3.474
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√1.737·(1.737-1)·(1.737-1)·(1.737-1.474)
=√1.737 · 0.737 · 0.737 · 0.263
=√0.248136437439
= 0.4981
Высота :
ha =
2S
a
=
2 · 0.4981
1
= 0.9962
hb =
2S
b
=
2 · 0.4981
1
= 0.9962
hc =
2S
c
=
2 · 0.4981
1.474
= 0.6758