В прямоугольном треугольнике со сторонами: a = 91.5, b = 216.63, с = 235.16, углы равны α° = 22.9°, β° = 67.1°, γ° = 90°
Ответ:
a=91.5
b=216.63
c=235.16
α°=22.9°
β°=67.1°
S = 9910.8
h=84.29
r = 36.49
R = 117.58
P = 543.29
Решение:
Гипотенуза:
c =
a
sin(α°)
=
91.5
sin(22.9°)
=
91.5
0.3891
= 235.16
Угол:
β° = 90°-α°
= 90°-22.9°
= 67.1°
Высота :
h = a·cos(α°)
= 91.5·cos(22.9°)
= 91.5·0.9212
= 84.29
Катет:
b = h·
c
a
= 84.29·
235.16
91.5
= 216.63
или:
b = √c2 - a2
= √235.162 - 91.52
= √55300.2 - 8372.3
= √46928
= 216.63
или:
b = c·sin(β°)
= 235.16·sin(67.1°)
= 235.16·0.9212
= 216.63
или:
b = c·cos(α°)
= 235.16·cos(22.9°)
= 235.16·0.9212
= 216.63
или:
b =
h
sin(α°)
=
84.29
sin(22.9°)
=
84.29
0.3891
= 216.63
или:
b =
h
cos(β°)
=
84.29
cos(67.1°)
=
84.29
0.3891
= 216.63
Площадь:
S =
h·c
2
=
84.29·235.16
2
= 9910.8
Радиус описанной окружности:
R =
c
2
=
235.16
2
= 117.58
Радиус вписанной окружности:
r =
a+b-c
2
=
91.5+216.63-235.16
2
= 36.49
Периметр:
P = a+b+c
= 91.5+216.63+235.16
= 543.29