В прямоугольном треугольнике со сторонами: a = 38.16, b = 16.2, с = 41.46, углы равны α° = 67°, β° = 23°, γ° = 90°
Ответ:
a=38.16
b=16.2
c=41.46
α°=67°
β°=23°
S = 309.08
h=14.91
r = 6.45
R = 20.73
P = 95.82
Решение:
Гипотенуза:
c =
b
sin(β°)
=
16.2
sin(23°)
=
16.2
0.3907
= 41.46
или:
c =
b
cos(α°)
=
16.2
cos(67°)
=
16.2
0.3907
= 41.46
Высота :
h = b·sin(α°)
= 16.2·sin(67°)
= 16.2·0.9205
= 14.91
или:
h = b·cos(β°)
= 16.2·cos(23°)
= 16.2·0.9205
= 14.91
Катет:
a = h·
c
b
= 14.91·
41.46
16.2
= 38.16
или:
a = √c2 - b2
= √41.462 - 16.22
= √1718.9 - 262.44
= √1456.5
= 38.16
или:
a = c·sin(α°)
= 41.46·sin(67°)
= 41.46·0.9205
= 38.16
или:
a = c·cos(β°)
= 41.46·cos(23°)
= 41.46·0.9205
= 38.16
или:
a =
h
cos(α°)
=
14.91
cos(67°)
=
14.91
0.3907
= 38.16
или:
a =
h
sin(β°)
=
14.91
sin(23°)
=
14.91
0.3907
= 38.16
Площадь:
S =
h·c
2
=
14.91·41.46
2
= 309.08
Радиус описанной окружности:
R =
c
2
=
41.46
2
= 20.73
Радиус вписанной окружности:
r =
a+b-c
2
=
38.16+16.2-41.46
2
= 6.45
Периметр:
P = a+b+c
= 38.16+16.2+41.46
= 95.82