В треугольнике со сторонами: a = 14.5, b = 0.7599, с = 14.52, углы равны α° = 87°, β° = 3°, γ° = 90°
Ответ:
a=14.5
b=0.7599
c=14.52
α°=87°
β°=3°
γ°=90°
S = 5.51
ha=0.76
hb=14.5
hc=0.7589
P = 29.78
Решение:
Сторона:
b = a·
sin(β°)
sin(α°)
= 14.5·
sin(3°)
sin(87°)
= 14.5·
0.05234
0.9986
= 14.5·0.05241
= 0.7599
Угол:
γ° = 180 - α° - β°
= 180 - 87° - 3°
= 90°
Высота :
hc = a·sin(β°)
= 14.5·sin(3°)
= 14.5·0.05234
= 0.7589
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √14.52 + 0.75992 - 2·14.5·0.7599·cos(90°)
= √210.25 + 0.5774 - 22.04·0
= √210.83
= 14.52
или:
c = a·
sin(γ°)
sin(α°)
= 14.5·
sin(90°)
sin(87°)
= 14.5·
1
0.9986
= 14.5·1.001
= 14.51
или:
c = b·
sin(γ°)
sin(β°)
= 0.7599·
sin(90°)
sin(3°)
= 0.7599·
1
0.05234
= 0.7599·19.11
= 14.52
Периметр:
P = a + b + c
= 14.5 + 0.7599 + 14.52
= 29.78
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√14.89·(14.89-14.5)·(14.89-0.7599)·(14.89-14.52)
=√14.89 · 0.39 · 14.1301 · 0.37
=√30.3603143727
= 5.51
Высота :
ha =
2S
a
=
2 · 5.51
14.5
= 0.76
hb =
2S
b
=
2 · 5.51
0.7599
= 14.5