В прямоугольном треугольнике со сторонами: a = 1.938, b = 0.5, с = 2.001, углы равны α° = 75.53°, β° = 14.47°, γ° = 90°
Ответ:
a=1.938
b=0.5
c=2.001
α°=75.53°
β°=14.47°
S = 0.4844
h=0.4842
r = 0.2185
R = 1.001
P = 4.439
Решение:
Гипотенуза:
c =
b
cos(α°)
=
0.5
cos(75.53°)
=
0.5
0.2499
= 2.001
Угол:
β° = 90°-α°
= 90°-75.53°
= 14.47°
Высота :
h = b·sin(α°)
= 0.5·sin(75.53°)
= 0.5·0.9683
= 0.4842
Катет:
a = h·
c
b
= 0.4842·
2.001
0.5
= 1.938
или:
a = √c2 - b2
= √2.0012 - 0.52
= √4.004 - 0.25
= √3.754
= 1.938
или:
a = c·sin(α°)
= 2.001·sin(75.53°)
= 2.001·0.9683
= 1.938
или:
a = c·cos(β°)
= 2.001·cos(14.47°)
= 2.001·0.9683
= 1.938
или:
a =
h
cos(α°)
=
0.4842
cos(75.53°)
=
0.4842
0.2499
= 1.938
или:
a =
h
sin(β°)
=
0.4842
sin(14.47°)
=
0.4842
0.2499
= 1.938
Площадь:
S =
h·c
2
=
0.4842·2.001
2
= 0.4844
Радиус описанной окружности:
R =
c
2
=
2.001
2
= 1.001
Радиус вписанной окружности:
r =
a+b-c
2
=
1.938+0.5-2.001
2
= 0.2185
Периметр:
P = a+b+c
= 1.938+0.5+2.001
= 4.439