В треугольнике со сторонами: a = 12, b = 16.78, с = 18.12, углы равны α° = 40°, β° = 64°, γ° = 76°
Ответ:
a=12
b=16.78
c=18.12
α°=40°
β°=64°
γ°=76°
S = 97.7
ha=16.28
hb=11.64
hc=10.79
P = 46.9
Решение:
Сторона:
b = a·
sin(β°)
sin(α°)
= 12·
sin(64°)
sin(40°)
= 12·
0.8988
0.6428
= 12·1.398
= 16.78
Угол:
γ° = 180 - α° - β°
= 180 - 40° - 64°
= 76°
Высота :
hc = a·sin(β°)
= 12·sin(64°)
= 12·0.8988
= 10.79
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √122 + 16.782 - 2·12·16.78·cos(76°)
= √144 + 281.57 - 402.72·0.2419
= √328.15
= 18.11
или:
c = a·
sin(γ°)
sin(α°)
= 12·
sin(76°)
sin(40°)
= 12·
0.9703
0.6428
= 12·1.509
= 18.11
или:
c = b·
sin(γ°)
sin(β°)
= 16.78·
sin(76°)
sin(64°)
= 16.78·
0.9703
0.8988
= 16.78·1.08
= 18.12
Периметр:
P = a + b + c
= 12 + 16.78 + 18.12
= 46.9
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√23.45·(23.45-12)·(23.45-16.78)·(23.45-18.12)
=√23.45 · 11.45 · 6.67 · 5.33
=√9545.55922775
= 97.7
Высота :
ha =
2S
a
=
2 · 97.7
12
= 16.28
hb =
2S
b
=
2 · 97.7
16.78
= 11.64