В треугольнике со сторонами: a = 2.652, b = 3, с = 2.03, углы равны α° = 60°, β° = 78.36°, γ° = 41.52°
Ответ:
a=2.652
b=3
c=2.03
α°=60°
β°=78.36°
γ°=41.52°
S = 2.637
ha=1.989
hb=1.758
hc=2.598
P = 7.682
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √32 + 2.032 - 2·3·2.03·cos(60°)
= √9 + 4.121 - 12.18·0.5
= √7.031
= 2.652
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3
2.652
sin(60°))
= arcsin(1.131·0.866)
= 78.36°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
2.03
2.652
sin(60°))
= arcsin(0.7655·0.866)
= 41.52°
Периметр:
P = a + b + c
= 2.652 + 3 + 2.03
= 7.682
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√3.841·(3.841-2.652)·(3.841-3)·(3.841-2.03)
=√3.841 · 1.189 · 0.841 · 1.811
=√6.955696241399
= 2.637
Высота :
ha =
2S
a
=
2 · 2.637
2.652
= 1.989
hb =
2S
b
=
2 · 2.637
3
= 1.758
hc =
2S
c
=
2 · 2.637
2.03
= 2.598