В треугольнике со сторонами: a = 100, b = 124, с = 169.88, углы равны α° = 35.67°, β° = 46.3°, γ° = 98.03°
Ответ:
a=100
b=124
c=169.88
α°=35.67°
β°=46.3°
γ°=98.03°
S = 6138.5
ha=122.77
hb=99.01
hc=72.3
P = 393.88
Решение:
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
100
124
sin(46.3°))
= arcsin(0.8065·0.723)
= 35.67°
Высота :
hc = a·sin(β°)
= 100·sin(46.3°)
= 100·0.723
= 72.3
Угол:
γ° = 180 - α° - β°
= 180 - 35.67° - 46.3°
= 98.03°
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √1002 + 1242 - 2·100·124·cos(98.03°)
= √10000 + 15376 - 24800·-0.1397
= √28840.6
= 169.83
или:
c = a·
sin(γ°)
sin(α°)
= 100·
sin(98.03°)
sin(35.67°)
= 100·
0.9902
0.5831
= 100·1.698
= 169.8
или:
c = b·
sin(γ°)
sin(β°)
= 124·
sin(98.03°)
sin(46.3°)
= 124·
0.9902
0.723
= 124·1.37
= 169.88
Периметр:
P = a + b + c
= 100 + 124 + 169.88
= 393.88
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√196.94·(196.94-100)·(196.94-124)·(196.94-169.88)
=√196.94 · 96.94 · 72.94 · 27.06
=√37681701.090227
= 6138.5
Высота :
ha =
2S
a
=
2 · 6138.5
100
= 122.77
hb =
2S
b
=
2 · 6138.5
124
= 99.01