В прямоугольном треугольнике со сторонами: a = 0.7333, b = 0.55, с = 0.9167, углы равны α° = 53.13°, β° = 36.87°, γ° = 90°
Ответ:
a=0.7333
b=0.55
c=0.9167
α°=53.13°
β°=36.87°
S = 0.2017
h=0.44
r = 0.1833
R = 0.4584
P = 2.2
Решение:
Гипотенуза:
c =
b
sin(β°)
=
0.55
sin(36.87°)
=
0.55
0.6
= 0.9167
или:
c =
b
cos(α°)
=
0.55
cos(53.13°)
=
0.55
0.6
= 0.9167
Высота :
h = b·sin(α°)
= 0.55·sin(53.13°)
= 0.55·0.8
= 0.44
или:
h = b·cos(β°)
= 0.55·cos(36.87°)
= 0.55·0.8
= 0.44
Катет:
a = h·
c
b
= 0.44·
0.9167
0.55
= 0.7334
или:
a = √c2 - b2
= √0.91672 - 0.552
= √0.8403 - 0.3025
= √0.5378
= 0.7333
или:
a = c·sin(α°)
= 0.9167·sin(53.13°)
= 0.9167·0.8
= 0.7334
или:
a = c·cos(β°)
= 0.9167·cos(36.87°)
= 0.9167·0.8
= 0.7334
или:
a =
h
cos(α°)
=
0.44
cos(53.13°)
=
0.44
0.6
= 0.7333
или:
a =
h
sin(β°)
=
0.44
sin(36.87°)
=
0.44
0.6
= 0.7333
Площадь:
S =
h·c
2
=
0.44·0.9167
2
= 0.2017
Радиус описанной окружности:
R =
c
2
=
0.9167
2
= 0.4584
Радиус вписанной окружности:
r =
a+b-c
2
=
0.7333+0.55-0.9167
2
= 0.1833
Периметр:
P = a+b+c
= 0.7333+0.55+0.9167
= 2.2