В прямоугольном треугольнике со сторонами: a = 4.3, b = 0.689, с = 4.355, углы равны α° = 80.9°, β° = 9.1°, γ° = 90°
Ответ:
a=4.3
b=0.689
c=4.355
α°=80.9°
β°=9.1°
S = 1.481
h=0.6803
r = 0.317
R = 2.178
P = 9.344
Решение:
Гипотенуза:
c =
a
cos(β°)
=
4.3
cos(9.1°)
=
4.3
0.9874
= 4.355
Угол:
α° = 90°-β°
= 90°-9.1°
= 80.9°
Высота :
h = a·sin(β°)
= 4.3·sin(9.1°)
= 4.3·0.1582
= 0.6803
Катет:
b = h·
c
a
= 0.6803·
4.355
4.3
= 0.689
или:
b = √c2 - a2
= √4.3552 - 4.32
= √18.97 - 18.49
= √0.476
= 0.6899
или:
b = c·sin(β°)
= 4.355·sin(9.1°)
= 4.355·0.1582
= 0.689
или:
b = c·cos(α°)
= 4.355·cos(80.9°)
= 4.355·0.1582
= 0.689
или:
b =
h
sin(α°)
=
0.6803
sin(80.9°)
=
0.6803
0.9874
= 0.689
или:
b =
h
cos(β°)
=
0.6803
cos(9.1°)
=
0.6803
0.9874
= 0.689
Площадь:
S =
h·c
2
=
0.6803·4.355
2
= 1.481
Радиус описанной окружности:
R =
c
2
=
4.355
2
= 2.178
Радиус вписанной окружности:
r =
a+b-c
2
=
4.3+0.689-4.355
2
= 0.317
Периметр:
P = a+b+c
= 4.3+0.689+4.355
= 9.344