В прямоугольном треугольнике со сторонами: a = 88.5, b = 2.271, с = 88.53, углы равны α° = 88.53°, β° = 1.47°, γ° = 90°
Ответ:
a=88.5
b=2.271
c=88.53
α°=88.53°
β°=1.47°
S = 100.48
h=2.27
r = 1.121
R = 44.27
P = 179.3
Решение:
Гипотенуза:
c =
a
cos(β°)
=
88.5
cos(1.47°)
=
88.5
0.9997
= 88.53
Угол:
α° = 90°-β°
= 90°-1.47°
= 88.53°
Высота :
h = a·sin(β°)
= 88.5·sin(1.47°)
= 88.5·0.02565
= 2.27
Катет:
b = h·
c
a
= 2.27·
88.53
88.5
= 2.271
или:
b = √c2 - a2
= √88.532 - 88.52
= √7837.6 - 7832.3
= √5.311
= 2.305
или:
b = c·sin(β°)
= 88.53·sin(1.47°)
= 88.53·0.02565
= 2.271
или:
b = c·cos(α°)
= 88.53·cos(88.53°)
= 88.53·0.02565
= 2.271
или:
b =
h
sin(α°)
=
2.27
sin(88.53°)
=
2.27
0.9997
= 2.271
или:
b =
h
cos(β°)
=
2.27
cos(1.47°)
=
2.27
0.9997
= 2.271
Площадь:
S =
h·c
2
=
2.27·88.53
2
= 100.48
Радиус описанной окружности:
R =
c
2
=
88.53
2
= 44.27
Радиус вписанной окружности:
r =
a+b-c
2
=
88.5+2.271-88.53
2
= 1.121
Периметр:
P = a+b+c
= 88.5+2.271+88.53
= 179.3