Решение:
Сторона:
c = a·
= 15·
= 15·
= 15·0.8165
= 12.25
Угол:
β° = 180 - γ° - α°
= 180 - 45° - 60°
= 75°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √152 + 12.252 - 2·15·12.25·cos(75°)
= √225 + 150.06 - 367.5·0.2588
= √279.95
= 16.73
или:
b = a·
= 15·
= 15·
= 15·1.115
= 16.73
или:
b = c·
= 12.25·
= 12.25·
= 12.25·1.366
= 16.73
Высота :
hc = a·sin(β°)
= 15·sin(75°)
= 15·0.9659
= 14.49
Периметр:
P = a + b + c
= 15 + 16.73 + 12.25
= 43.98
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√21.99·(21.99-15)·(21.99-16.73)·(21.99-12.25)
=√21.99 · 6.99 · 5.26 · 9.74
=√7874.93732724
= 88.74
Высота :
ha =
=
= 11.83
hb =
=
= 10.61