В треугольнике со сторонами: a = 9, b = 41, с = 41.98, углы равны α° = 12.38°, β° = 77.61°, γ° = 90°
Ответ:
a=9
b=41
c=41.98
α°=12.38°
β°=77.61°
γ°=90°
S = 184.5
ha=41
hb=9
hc=8.79
P = 91.98
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √92 + 412 - 2·9·41·cos(90°)
= √81 + 1681 - 738·0
= √1762
= 41.98
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
9
41.98
sin(90°))
= arcsin(0.2144·1)
= 12.38°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
412+41.982-92
2·41·41.98
)
= arccos(
1681+1762.3204-81
3442.4
)
= 12.38°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
41
41.98
sin(90°))
= arcsin(0.9767·1)
= 77.61°
Периметр:
P = a + b + c
= 9 + 41 + 41.98
= 91.98
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√45.99·(45.99-9)·(45.99-41)·(45.99-41.98)
=√45.99 · 36.99 · 4.99 · 4.01
=√34040.24358399
= 184.5
Высота :
ha =
2S
a
=
2 · 184.5
9
= 41
hb =
2S
b
=
2 · 184.5
41
= 9
hc =
2S
c
=
2 · 184.5
41.98
= 8.79