В треугольнике со сторонами: a = 35.8, b = 42.28, с = 11.5, углы равны α° = 48.98°, β° = 117°, γ° = 14.03°
Ответ:
a=35.8
b=42.28
c=11.5
α°=48.98°
β°=117°
γ°=14.03°
S = 183.43
ha=10.25
hb=8.677
hc=31.9
P = 89.58
Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √35.82 + 11.52 - 2·35.8·11.5·cos(117°)
= √1281.6 + 132.25 - 823.4·-0.454
= √1787.7
= 42.28
Высота :
hc = a·sin(β°)
= 35.8·sin(117°)
= 35.8·0.891
= 31.9
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
35.8
42.28
sin(117°))
= arcsin(0.8467·0.891)
= 48.97°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
42.282+11.52-35.82
2·42.28·11.5
)
= arccos(
1787.5984+132.25-1281.64
972.44
)
= 48.98°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
11.5
42.28
sin(117°))
= arcsin(0.272·0.891)
= 14.03°
Периметр:
P = a + b + c
= 35.8 + 42.28 + 11.5
= 89.58
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√44.79·(44.79-35.8)·(44.79-42.28)·(44.79-11.5)
=√44.79 · 8.99 · 2.51 · 33.29
=√33645.59948559
= 183.43
Высота :
ha =
2S
a
=
2 · 183.43
35.8
= 10.25
hb =
2S
b
=
2 · 183.43
42.28
= 8.677