В прямоугольном треугольнике со сторонами: a = 1.001, b = 3.889, с = 4.015 высота равна h = 0.9691
Ответ:
a=1.001
b=3.889
c=4.015
α°=14.43°
β°=75.57°
S = 1.945
h=0.9691
r = 0.4375
R = 2.008
P = 8.905
Решение:
Гипотенуза:
c =
b
cos(α°)
=
3.889
cos(14.43°)
=
3.889
0.9685
= 4.015
Угол:
β° = 90°-α°
= 90°-14.43°
= 75.57°
Высота :
h = b·sin(α°)
= 3.889·sin(14.43°)
= 3.889·0.2492
= 0.9691
Катет:
a = h·
c
b
= 0.9691·
4.015
3.889
= 1
или:
a = √c2 - b2
= √4.0152 - 3.8892
= √16.12 - 15.12
= √0.9959
= 0.9979
или:
a = c·sin(α°)
= 4.015·sin(14.43°)
= 4.015·0.2492
= 1.001
или:
a = c·cos(β°)
= 4.015·cos(75.57°)
= 4.015·0.2492
= 1.001
или:
a =
h
cos(α°)
=
0.9691
cos(14.43°)
=
0.9691
0.9685
= 1.001
или:
a =
h
sin(β°)
=
0.9691
sin(75.57°)
=
0.9691
0.9685
= 1.001
Площадь:
S =
h·c
2
=
0.9691·4.015
2
= 1.945
Радиус описанной окружности:
R =
c
2
=
4.015
2
= 2.008
Радиус вписанной окружности:
r =
a+b-c
2
=
1.001+3.889-4.015
2
= 0.4375
Периметр:
P = a+b+c
= 1.001+3.889+4.015
= 8.905