В прямоугольном треугольнике со сторонами: a = 0.9557, b = 78.2, с = 78.21 высота равна h = 0.9556
Ответ:
a=0.9557
b=78.2
c=78.21
α°=0.7°
β°=89.3°
S = 37.37
h=0.9556
r = 0.4729
R = 39.11
P = 157.37
Решение:
Гипотенуза:
c =
b
cos(α°)
=
78.2
cos(0.7°)
=
78.2
0.9999
= 78.21
Угол:
β° = 90°-α°
= 90°-0.7°
= 89.3°
Высота :
h = b·sin(α°)
= 78.2·sin(0.7°)
= 78.2·0.01222
= 0.9556
Катет:
a = h·
c
b
= 0.9556·
78.21
78.2
= 0.9557
или:
a = √c2 - b2
= √78.212 - 78.22
= √6116.8 - 6115.2
= √1.564
= 1.251
или:
a = c·sin(α°)
= 78.21·sin(0.7°)
= 78.21·0.01222
= 0.9557
или:
a = c·cos(β°)
= 78.21·cos(89.3°)
= 78.21·0.01222
= 0.9557
или:
a =
h
cos(α°)
=
0.9556
cos(0.7°)
=
0.9556
0.9999
= 0.9557
или:
a =
h
sin(β°)
=
0.9556
sin(89.3°)
=
0.9556
0.9999
= 0.9557
Площадь:
S =
h·c
2
=
0.9556·78.21
2
= 37.37
Радиус описанной окружности:
R =
c
2
=
78.21
2
= 39.11
Радиус вписанной окружности:
r =
a+b-c
2
=
0.9557+78.2-78.21
2
= 0.4729
Периметр:
P = a+b+c
= 0.9557+78.2+78.21
= 157.37