В прямоугольном треугольнике со сторонами: a = 0.75, b = 0.60, с = 0.9605, углы равны α° = 51.34°, β° = 38.66°, γ° = 90°
Ответ:
a=0.75
b=0.60
c=0.9605
α°=51.34°
β°=38.66°
S = 0.225
h=0.4685
r = 0.1948
R = 0.4803
P = 2.311
Решение:
Гипотенуза:
c =
b
cos(α°)
=
0.60
cos(51.34°)
=
0.60
0.6247
= 0.9605
Угол:
β° = 90°-α°
= 90°-51.34°
= 38.66°
Высота :
h = b·sin(α°)
= 0.60·sin(51.34°)
= 0.60·0.7809
= 0.4685
Катет:
a = h·
c
b
= 0.4685·
0.9605
0.60
= 0.75
или:
a = √c2 - b2
= √0.96052 - 0.602
= √0.9226 - 0.36
= √0.5626
= 0.7501
или:
a = c·sin(α°)
= 0.9605·sin(51.34°)
= 0.9605·0.7809
= 0.7501
или:
a = c·cos(β°)
= 0.9605·cos(38.66°)
= 0.9605·0.7809
= 0.7501
или:
a =
h
cos(α°)
=
0.4685
cos(51.34°)
=
0.4685
0.6247
= 0.75
или:
a =
h
sin(β°)
=
0.4685
sin(38.66°)
=
0.4685
0.6247
= 0.75
Площадь:
S =
h·c
2
=
0.4685·0.9605
2
= 0.225
Радиус описанной окружности:
R =
c
2
=
0.9605
2
= 0.4803
Радиус вписанной окружности:
r =
a+b-c
2
=
0.75+0.60-0.9605
2
= 0.1948
Периметр:
P = a+b+c
= 0.75+0.60+0.9605
= 2.311