В прямоугольном треугольнике со сторонами: a = 38.1, b = 0.6649, с = 38.11, углы равны α° = 89°, β° = 1°, γ° = 90°
Ответ:
a=38.1
b=0.6649
c=38.11
α°=89°
β°=1°
S = 12.67
h=0.6648
r = 0.3275
R = 19.06
P = 76.87
Решение:
Гипотенуза:
c =
a
cos(β°)
=
38.1
cos(1°)
=
38.1
0.9998
= 38.11
Угол:
α° = 90°-β°
= 90°-1°
= 89°
Высота :
h = a·sin(β°)
= 38.1·sin(1°)
= 38.1·0.01745
= 0.6648
Катет:
b = h·
c
a
= 0.6648·
38.11
38.1
= 0.665
или:
b = √c2 - a2
= √38.112 - 38.12
= √1452.4 - 1451.6
= √0.7621
= 0.873
или:
b = c·sin(β°)
= 38.11·sin(1°)
= 38.11·0.01745
= 0.665
или:
b = c·cos(α°)
= 38.11·cos(89°)
= 38.11·0.01745
= 0.665
или:
b =
h
sin(α°)
=
0.6648
sin(89°)
=
0.6648
0.9998
= 0.6649
или:
b =
h
cos(β°)
=
0.6648
cos(1°)
=
0.6648
0.9998
= 0.6649
Площадь:
S =
h·c
2
=
0.6648·38.11
2
= 12.67
Радиус описанной окружности:
R =
c
2
=
38.11
2
= 19.06
Радиус вписанной окружности:
r =
a+b-c
2
=
38.1+0.6649-38.11
2
= 0.3275
Периметр:
P = a+b+c
= 38.1+0.6649+38.11
= 76.87