В прямоугольном треугольнике со сторонами: a = 0.6917, b = 0.65, с = 0.9492 высота равна h = 0.4737
Ответ:
a=0.6917
b=0.65
c=0.9492
α°=46.78°
β°=43.22°
S = 0.2248
h=0.4737
r = 0.1963
R = 0.4746
P = 2.291
Решение:
Гипотенуза:
c =
b
cos(α°)
=
0.65
cos(46.78°)
=
0.65
0.6848
= 0.9492
Угол:
β° = 90°-α°
= 90°-46.78°
= 43.22°
Высота :
h = b·sin(α°)
= 0.65·sin(46.78°)
= 0.65·0.7287
= 0.4737
Катет:
a = h·
c
b
= 0.4737·
0.9492
0.65
= 0.6917
или:
a = √c2 - b2
= √0.94922 - 0.652
= √0.901 - 0.4225
= √0.4785
= 0.6917
или:
a = c·sin(α°)
= 0.9492·sin(46.78°)
= 0.9492·0.7287
= 0.6917
или:
a = c·cos(β°)
= 0.9492·cos(43.22°)
= 0.9492·0.7287
= 0.6917
или:
a =
h
cos(α°)
=
0.4737
cos(46.78°)
=
0.4737
0.6848
= 0.6917
или:
a =
h
sin(β°)
=
0.4737
sin(43.22°)
=
0.4737
0.6848
= 0.6917
Площадь:
S =
h·c
2
=
0.4737·0.9492
2
= 0.2248
Радиус описанной окружности:
R =
c
2
=
0.9492
2
= 0.4746
Радиус вписанной окружности:
r =
a+b-c
2
=
0.6917+0.65-0.9492
2
= 0.1963
Периметр:
P = a+b+c
= 0.6917+0.65+0.9492
= 2.291