Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √1.52 + 1.62 - 2·1.5·1.6·cos(90°)
= √2.25 + 2.56 - 4.8·0
= √4.81
= 2.193
Угол:
α° = arcsin(
sin(γ°))
= arcsin(
sin(90°))
= arcsin(0.684·1)
= 43.16°
или:
α° = arccos(
)
= arccos(
1.62+2.1932-1.52
2·1.6·2.193
)
= arccos(
)
= 43.16°
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(90°))
= arcsin(0.7296·1)
= 46.85°
Периметр:
P = a + b + c
= 1.5 + 1.6 + 2.193
= 5.293
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√2.647·(2.647-1.5)·(2.647-1.6)·(2.647-2.193)
=√2.647 · 1.147 · 1.047 · 0.454
=√1.443177979842
= 1.201
Высота :
ha =
=
= 1.601
hb =
=
= 1.501
hc =
=
= 1.095