В треугольнике со сторонами: a = 150, b = 169.63, с = 140, углы равны α° = 56.99°, β° = 71.5°, γ° = 51.5°
Ответ:
a=150
b=169.63
c=140
α°=56.99°
β°=71.5°
γ°=51.5°
S = 9958.6
ha=132.78
hb=117.42
hc=142.25
P = 459.63
Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √1502 + 1402 - 2·150·140·cos(71.5°)
= √22500 + 19600 - 42000·0.3173
= √28773.4
= 169.63
Высота :
hc = a·sin(β°)
= 150·sin(71.5°)
= 150·0.9483
= 142.25
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
150
169.63
sin(71.5°))
= arcsin(0.8843·0.9483)
= 56.99°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
169.632+1402-1502
2·169.63·140
)
= arccos(
28774.3369+19600-22500
47496.4
)
= 56.99°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
140
169.63
sin(71.5°))
= arcsin(0.8253·0.9483)
= 51.5°
Периметр:
P = a + b + c
= 150 + 169.63 + 140
= 459.63
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√229.82·(229.82-150)·(229.82-169.63)·(229.82-140)
=√229.82 · 79.82 · 60.19 · 89.82
=√99173796.251372
= 9958.6
Высота :
ha =
2S
a
=
2 · 9958.6
150
= 132.78
hb =
2S
b
=
2 · 9958.6
169.63
= 117.42