В треугольнике со сторонами: a = 15, b = 25, с = 29.15, углы равны α° = 30.97°, β° = 59.05°, γ° = 90°
Ответ:
a=15
b=25
c=29.15
α°=30.97°
β°=59.05°
γ°=90°
S = 187.67
ha=25.02
hb=15.01
hc=12.88
P = 69.15
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √152 + 252 - 2·15·25·cos(90°)
= √225 + 625 - 750·0
= √850
= 29.15
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
15
29.15
sin(90°))
= arcsin(0.5146·1)
= 30.97°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
252+29.152-152
2·25·29.15
)
= arccos(
625+849.7225-225
1457.5
)
= 30.97°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
25
29.15
sin(90°))
= arcsin(0.8576·1)
= 59.05°
Периметр:
P = a + b + c
= 15 + 25 + 29.15
= 69.15
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√34.58·(34.58-15)·(34.58-25)·(34.58-29.15)
=√34.58 · 19.58 · 9.58 · 5.43
=√35221.10808216
= 187.67
Высота :
ha =
2S
a
=
2 · 187.67
15
= 25.02
hb =
2S
b
=
2 · 187.67
25
= 15.01
hc =
2S
c
=
2 · 187.67
29.15
= 12.88