В треугольнике со сторонами: a = 59, b = 61, с = 84.86, углы равны α° = 44.05°, β° = 45.96°, γ° = 90°
Ответ:
a=59
b=61
c=84.86
α°=44.05°
β°=45.96°
γ°=90°
S = 1799.5
ha=61
hb=59
hc=42.41
P = 204.86
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √592 + 612 - 2·59·61·cos(90°)
= √3481 + 3721 - 7198·0
= √7202
= 84.86
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
59
84.86
sin(90°))
= arcsin(0.6953·1)
= 44.05°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
612+84.862-592
2·61·84.86
)
= arccos(
3721+7201.2196-3481
10352.9
)
= 44.05°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
61
84.86
sin(90°))
= arcsin(0.7188·1)
= 45.96°
Периметр:
P = a + b + c
= 59 + 61 + 84.86
= 204.86
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√102.43·(102.43-59)·(102.43-61)·(102.43-84.86)
=√102.43 · 43.43 · 41.43 · 17.57
=√3238200.211936
= 1799.5
Высота :
ha =
2S
a
=
2 · 1799.5
59
= 61
hb =
2S
b
=
2 · 1799.5
61
= 59
hc =
2S
c
=
2 · 1799.5
84.86
= 42.41