В прямоугольном треугольнике со сторонами: a = 9.332, b = 9.208, с = 13.11, углы равны α° = 45.38°, β° = 44.62°, γ° = 90°
Ответ:
a=9.332
b=9.208
c=13.11
α°=45.38°
β°=44.62°
S = 42.96
h=6.555
r = 2.715
R = 6.555
P = 31.65
Решение:
Катет:
a = c·sin(α°)
= 13.11·sin(45.38°)
= 13.11·0.7118
= 9.332
или:
a = c·cos(β°)
= 13.11·cos(44.62°)
= 13.11·0.7118
= 9.332
Катет:
b = c·sin(β°)
= 13.11·sin(44.62°)
= 13.11·0.7024
= 9.208
или:
b = c·cos(α°)
= 13.11·cos(45.38°)
= 13.11·0.7024
= 9.208
Радиус описанной окружности:
R =
c
2
=
13.11
2
= 6.555
Высота :
h =
ab
c
=
9.332·9.208
13.11
= 6.554
или:
h = b·sin(α°)
= 9.208·sin(45.38°)
= 9.208·0.7118
= 6.554
или:
h = b·cos(β°)
= 9.208·cos(44.62°)
= 9.208·0.7118
= 6.554
или:
h = a·cos(α°)
= 9.332·cos(45.38°)
= 9.332·0.7024
= 6.555
или:
h = a·sin(β°)
= 9.332·sin(44.62°)
= 9.332·0.7024
= 6.555
Площадь:
S =
ab
2
=
9.332·9.208
2
= 42.96
Радиус вписанной окружности:
r =
a+b-c
2
=
9.332+9.208-13.11
2
= 2.715
Периметр:
P = a+b+c
= 9.332+9.208+13.11
= 31.65