В прямоугольном треугольнике со сторонами: a = 50.75, b = 15.52, с = 53.08, углы равны α° = 73°, β° = 17°, γ° = 90°
Ответ:
a=50.75
b=15.52
c=53.08
α°=73°
β°=17°
S = 393.85
h=14.84
r = 6.595
R = 26.54
P = 119.35
Решение:
Гипотенуза:
c =
b
sin(β°)
=
15.52
sin(17°)
=
15.52
0.2924
= 53.08
или:
c =
b
cos(α°)
=
15.52
cos(73°)
=
15.52
0.2924
= 53.08
Высота :
h = b·sin(α°)
= 15.52·sin(73°)
= 15.52·0.9563
= 14.84
или:
h = b·cos(β°)
= 15.52·cos(17°)
= 15.52·0.9563
= 14.84
Катет:
a = h·
c
b
= 14.84·
53.08
15.52
= 50.75
или:
a = √c2 - b2
= √53.082 - 15.522
= √2817.5 - 240.87
= √2576.6
= 50.76
или:
a = c·sin(α°)
= 53.08·sin(73°)
= 53.08·0.9563
= 50.76
или:
a = c·cos(β°)
= 53.08·cos(17°)
= 53.08·0.9563
= 50.76
или:
a =
h
cos(α°)
=
14.84
cos(73°)
=
14.84
0.2924
= 50.75
или:
a =
h
sin(β°)
=
14.84
sin(17°)
=
14.84
0.2924
= 50.75
Площадь:
S =
h·c
2
=
14.84·53.08
2
= 393.85
Радиус описанной окружности:
R =
c
2
=
53.08
2
= 26.54
Радиус вписанной окружности:
r =
a+b-c
2
=
50.75+15.52-53.08
2
= 6.595
Периметр:
P = a+b+c
= 50.75+15.52+53.08
= 119.35