Решение:
Сторона:
b = √0.25·a2 + h2
= √0.25·80002 + 20002
= √16000000 + 4000000
= √20000000
= 4472.1
Угол:
α° = 2·arcsin
= 2·arcsin
= 126.87°
Угол:
β° = arccos
= 2·arccos
= 26.56°
Площадь:
S =
√4· b2 - a2
=
√4· 4472.12 - 80002
=
√4· 19999678.41 - 64000000
=
√79998713.64 - 64000000
=
√15998713.64
= 7999678
Радиус вписанной окружности:
r =
=
·
√2·4472.1-8000
2·4472.1+8000
=4000·√0.05572
= 944.2
Радиус описанной окружности:
R =
=
4472.12
√4·4472.12 - 80002
=
19999678
√79998712 - 64000000
=
= 5000.2
Периметр:
P = a + 2b
= 8000 + 2·4472.1
= 16944.2