В треугольнике со сторонами: a = 2.45, b = 3, с = 3.346, углы равны α° = 45°, β° = 59.94°, γ° = 74.99°
Ответ:
a=2.45
b=3
c=3.346
α°=45°
β°=59.94°
γ°=74.99°
S = 3.55
ha=2.898
hb=2.367
hc=2.122
P = 8.796
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √32 + 3.3462 - 2·3·3.346·cos(45°)
= √9 + 11.2 - 20.08·0.7071
= √6.001
= 2.45
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
3
2.45
sin(45°))
= arcsin(1.224·0.7071)
= 59.94°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
3.346
2.45
sin(45°))
= arcsin(1.366·0.7071)
= 74.99°
Периметр:
P = a + b + c
= 2.45 + 3 + 3.346
= 8.796
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√4.398·(4.398-2.45)·(4.398-3)·(4.398-3.346)
=√4.398 · 1.948 · 1.398 · 1.052
=√12.599899723584
= 3.55
Высота :
ha =
2S
a
=
2 · 3.55
2.45
= 2.898
hb =
2S
b
=
2 · 3.55
3
= 2.367
hc =
2S
c
=
2 · 3.55
3.346
= 2.122