В треугольнике со сторонами: a = 11.5, b = 35.8, с = 41.66, углы равны α° = 14.72°, β° = 52.28°, γ° = 113°
Ответ:
a=11.5
b=35.8
c=41.66
α°=14.72°
β°=52.28°
γ°=113°
S = 189.49
ha=32.95
hb=10.59
hc=9.097
P = 88.96
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √11.52 + 35.82 - 2·11.5·35.8·cos(113°)
= √132.25 + 1281.6 - 823.4·-0.3907
= √1735.6
= 41.66
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
11.5
41.66
sin(113°))
= arcsin(0.276·0.9205)
= 14.72°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
35.82+41.662-11.52
2·35.8·41.66
)
= arccos(
1281.64+1735.5556-132.25
2982.9
)
= 14.72°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
35.8
41.66
sin(113°))
= arcsin(0.8593·0.9205)
= 52.28°
Периметр:
P = a + b + c
= 11.5 + 35.8 + 41.66
= 88.96
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√44.48·(44.48-11.5)·(44.48-35.8)·(44.48-41.66)
=√44.48 · 32.98 · 8.68 · 2.82
=√35907.42511104
= 189.49
Высота :
ha =
2S
a
=
2 · 189.49
11.5
= 32.95
hb =
2S
b
=
2 · 189.49
35.8
= 10.59
hc =
2S
c
=
2 · 189.49
41.66
= 9.097