Решение:
Угол:
β° = arcsin(
sin(γ°))
= arcsin(
sin(90°))
= arcsin(0.5102·1)
= 30.68°
Угол:
α° = 180 - γ° - β°
= 180 - 90° - 30.68°
= 59.32°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √52 + 9.82 - 2·5·9.8·cos(59.32°)
= √25 + 96.04 - 98·0.5102
= √71.04
= 8.429
или:
a = b·
= 5·
= 5·
= 5·1.686
= 8.43
или:
a = c·
= 9.8·
= 9.8·
= 9.8·0.86
= 8.428
Периметр:
P = a + b + c
= 8.428 + 5 + 9.8
= 23.23
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√11.61·(11.61-8.428)·(11.61-5)·(11.61-9.8)
=√11.61 · 3.182 · 6.61 · 1.81
=√441.989985582
= 21.02
hb =
=
= 8.408
hc =
=
= 4.29