В прямоугольном треугольнике со сторонами: a = 15.96, b = 51.9, с = 54.3, углы равны α° = 17.1°, β° = 72.9°, γ° = 90°
Ответ:
a=15.96
b=51.9
c=54.3
α°=17.1°
β°=72.9°
S = 414.16
h=15.25
r = 6.78
R = 27.15
P = 122.16
Решение:
Катет:
a = c·sin(α°)
= 54.3·sin(17.1°)
= 54.3·0.294
= 15.96
Катет:
b = c·cos(α°)
= 54.3·cos(17.1°)
= 54.3·0.9558
= 51.9
Угол:
β° = 90°-α°
= 90°-17.1°
= 72.9°
Радиус описанной окружности:
R =
c
2
=
54.3
2
= 27.15
Высота :
h =
ab
c
=
15.96·51.9
54.3
= 15.25
или:
h = b·sin(α°)
= 51.9·sin(17.1°)
= 51.9·0.294
= 15.26
или:
h = b·cos(β°)
= 51.9·cos(72.9°)
= 51.9·0.294
= 15.26
или:
h = a·cos(α°)
= 15.96·cos(17.1°)
= 15.96·0.9558
= 15.25
или:
h = a·sin(β°)
= 15.96·sin(72.9°)
= 15.96·0.9558
= 15.25
Площадь:
S =
ab
2
=
15.96·51.9
2
= 414.16
Радиус вписанной окружности:
r =
a+b-c
2
=
15.96+51.9-54.3
2
= 6.78
Периметр:
P = a+b+c
= 15.96+51.9+54.3
= 122.16