Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √24.9952 + 11.912 - 2·24.995·11.91·cos(74°)
= √624.75 + 141.85 - 595.38·0.2756
= √602.51
= 24.55
Высота :
hc = a·sin(β°)
= 24.995·sin(74°)
= 24.995·0.9613
= 24.03
Угол:
α° = arcsin(
sin(β°))
= arcsin(
sin(74°))
= arcsin(1.018·0.9613)
= 78.13°
или:
α° = arccos(
)
= arccos(
24.552+11.912-24.9952
2·24.55·11.91
)
= arccos(
602.7025+141.8481-624.750025
584.78
)
= 78.18°
Угол:
γ° = arcsin(
sin(α°))
= arcsin(
sin(74°))
= arcsin(0.4851·0.9613)
= 27.8°
Периметр:
P = a + b + c
= 24.995 + 24.55 + 11.91
= 61.46
Площадь:
p =
S =√p·(p-a)·(p-b)·(p-c)
=√30.73·(30.73-24.995)·(30.73-24.55)·(30.73-11.91)
=√30.73 · 5.735 · 6.18 · 18.82
=√20497.65016278
= 143.17
Высота :
ha =
=
= 11.46
hb =
=
= 11.66