В треугольнике со сторонами: a = 42.78, b = 23.8, с = 23.4, углы равны α° = 130°, β° = 25.22°, γ° = 24.77°
Ответ:
a=42.78
b=23.8
c=23.4
α°=130°
β°=25.22°
γ°=24.77°
S = 213.28
ha=9.971
hb=17.92
hc=18.23
P = 89.98
Решение:
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √23.82 + 23.42 - 2·23.8·23.4·cos(130°)
= √566.44 + 547.56 - 1113.8·-0.6428
= √1830
= 42.78
Угол:
β° = arcsin(
b
a
sin(α°))
= arcsin(
23.8
42.78
sin(130°))
= arcsin(0.5563·0.766)
= 25.22°
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
23.4
42.78
sin(130°))
= arcsin(0.547·0.766)
= 24.77°
Периметр:
P = a + b + c
= 42.78 + 23.8 + 23.4
= 89.98
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√44.99·(44.99-42.78)·(44.99-23.8)·(44.99-23.4)
=√44.99 · 2.21 · 21.19 · 21.59
=√45487.47876959
= 213.28
Высота :
ha =
2S
a
=
2 · 213.28
42.78
= 9.971
hb =
2S
b
=
2 · 213.28
23.8
= 17.92
hc =
2S
c
=
2 · 213.28
23.4
= 18.23