В прямоугольном треугольнике со сторонами: a = 0.007, b = 0.01038, с = 0.01252, углы равны α° = 33°, β° = 56°, γ° = 90°
Ответ:
a=0.007
b=0.01038
c=0.01252
α°=33°
β°=56°
S = 3.633E-5
h=0.005803
r = 0.00243
R = 0.00626
P = 0.0299
Решение:
Гипотенуза:
c =
a
sin(α°)
=
0.007
sin(33°)
=
0.007
0.5446
= 0.01285
или:
c =
a
cos(β°)
=
0.007
cos(56°)
=
0.007
0.5592
= 0.01252
Высота :
h = a·cos(α°)
= 0.007·cos(33°)
= 0.007·0.8387
= 0.005871
или:
h = a·sin(β°)
= 0.007·sin(56°)
= 0.007·0.829
= 0.005803
Катет:
b = h·
c
a
= 0.005803·
0.01252
0.007
= 0.01038
или:
b = √c2 - a2
= √0.012522 - 0.0072
= √0.0001568 - 4.9E-5
= √0.0001078
= 0.01038
или:
b = c·sin(β°)
= 0.01252·sin(56°)
= 0.01252·0.829
= 0.01038
или:
b = c·cos(α°)
= 0.01252·cos(33°)
= 0.01252·0.8387
= 0.0105
или:
b =
h
sin(α°)
=
0.005803
sin(33°)
=
0.005803
0.5446
= 0.01066
или:
b =
h
cos(β°)
=
0.005803
cos(56°)
=
0.005803
0.5592
= 0.01038
Площадь:
S =
h·c
2
=
0.005803·0.01252
2
= 3.633E-5
Радиус описанной окружности:
R =
c
2
=
0.01252
2
= 0.00626
Радиус вписанной окружности:
r =
a+b-c
2
=
0.007+0.01038-0.01252
2
= 0.00243
Периметр:
P = a+b+c
= 0.007+0.01038+0.01252
= 0.0299