В треугольнике со сторонами: a = 61, b = 85.12, с = 70, углы равны α° = 45°, β° = 80.73°, γ° = 54.27°
Ответ:
a=61
b=85.12
c=70
α°=45°
β°=80.73°
γ°=54.27°
S = 2107.1
ha=69.09
hb=49.51
hc=60.2
P = 216.12
Решение:
Угол:
γ° = arcsin(
c
a
sin(α°))
= arcsin(
70
61
sin(45°))
= arcsin(1.148·0.7071)
= 54.27°
Угол:
β° = 180 - γ° - α°
= 180 - 54.27° - 45°
= 80.73°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √612 + 702 - 2·61·70·cos(80.73°)
= √3721 + 4900 - 8540·0.1611
= √7245.2
= 85.12
или:
b = a·
sin(β°)
sin(α°)
= 61·
sin(80.73°)
sin(45°)
= 61·
0.9869
0.7071
= 61·1.396
= 85.16
или:
b = c·
sin(β°)
sin(γ°)
= 70·
sin(80.73°)
sin(54.27°)
= 70·
0.9869
0.8118
= 70·1.216
= 85.12
Высота :
hc = a·sin(β°)
= 61·sin(80.73°)
= 61·0.9869
= 60.2
Периметр:
P = a + b + c
= 61 + 85.12 + 70
= 216.12
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√108.06·(108.06-61)·(108.06-85.12)·(108.06-70)
=√108.06 · 47.06 · 22.94 · 38.06
=√4439960.266067
= 2107.1
Высота :
ha =
2S
a
=
2 · 2107.1
61
= 69.09
hb =
2S
b
=
2 · 2107.1
85.12
= 49.51