Решение:
Угол:
β° = arcsin(
sin(α°))
= arcsin(
sin(50°))
= arcsin(1·0.766)
= 50°
Угол:
γ° = 180 - α° - β°
= 180 - 50° - 50°
= 80°
Высота :
hc = a·sin(β°)
= 25·sin(50°)
= 25·0.766
= 19.15
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √252 + 252 - 2·25·25·cos(80°)
= √625 + 625 - 1250·0.1736
= √1033
= 32.14
или:
c = a·
= 25·
= 25·
= 25·1.286
= 32.15
или:
c = b·
= 25·
= 25·
= 25·1.286
= 32.15
Периметр:
P = a + b + c
= 25 + 25 + 32.15
= 82.15
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√41.08·(41.08-25)·(41.08-25)·(41.08-32.15)
=√41.08 · 16.08 · 16.08 · 8.93
=√94853.63586816
= 307.98
Высота :
ha =
=
= 24.64
hb =
=
= 24.64