В прямоугольном треугольнике со сторонами: a = 1.834, b = 1.1, с = 2.138, углы равны α° = 59.03°, β° = 30.96°, γ° = 90°
Ответ:
a=1.834
b=1.1
c=2.138
α°=59.03°
β°=30.96°
S = 1.008
h=0.9433
r = 0.398
R = 1.069
P = 5.072
Решение:
Гипотенуза:
c =
b
sin(β°)
=
1.1
sin(30.96°)
=
1.1
0.5144
= 2.138
или:
c =
b
cos(α°)
=
1.1
cos(59.03°)
=
1.1
0.5146
= 2.138
Высота :
h = b·sin(α°)
= 1.1·sin(59.03°)
= 1.1·0.8574
= 0.9431
или:
h = b·cos(β°)
= 1.1·cos(30.96°)
= 1.1·0.8575
= 0.9433
Катет:
a = h·
c
b
= 0.9433·
2.138
1.1
= 1.833
или:
a = √c2 - b2
= √2.1382 - 1.12
= √4.571 - 1.21
= √3.361
= 1.833
или:
a = c·sin(α°)
= 2.138·sin(59.03°)
= 2.138·0.8574
= 1.833
или:
a = c·cos(β°)
= 2.138·cos(30.96°)
= 2.138·0.8575
= 1.833
или:
a =
h
cos(α°)
=
0.9433
cos(59.03°)
=
0.9433
0.5146
= 1.833
или:
a =
h
sin(β°)
=
0.9433
sin(30.96°)
=
0.9433
0.5144
= 1.834
Площадь:
S =
h·c
2
=
0.9433·2.138
2
= 1.008
Радиус описанной окружности:
R =
c
2
=
2.138
2
= 1.069
Радиус вписанной окружности:
r =
a+b-c
2
=
1.834+1.1-2.138
2
= 0.398
Периметр:
P = a+b+c
= 1.834+1.1+2.138
= 5.072