В треугольнике со сторонами: a = 15, b = 14.17, с = 20, углы равны α° = 48.47°, β° = 45°, γ° = 86.13°
Ответ:
a=15
b=14.17
c=20
α°=48.47°
β°=45°
γ°=86.13°
S = 106.2
ha=14.16
hb=14.99
hc=10.61
P = 49.17
Решение:
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √152 + 202 - 2·15·20·cos(45°)
= √225 + 400 - 600·0.7071
= √200.74
= 14.17
Высота :
hc = a·sin(β°)
= 15·sin(45°)
= 15·0.7071
= 10.61
Угол:
α° = arcsin(
a
b
sin(β°))
= arcsin(
15
14.17
sin(45°))
= arcsin(1.059·0.7071)
= 48.49°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
14.172+202-152
2·14.17·20
)
= arccos(
200.7889+400-225
566.8
)
= 48.47°
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
20
14.17
sin(45°))
= arcsin(1.411·0.7071)
= 86.13°
Периметр:
P = a + b + c
= 15 + 14.17 + 20
= 49.17
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√24.59·(24.59-15)·(24.59-14.17)·(24.59-20)
=√24.59 · 9.59 · 10.42 · 4.59
=√11278.66092318
= 106.2
Высота :
ha =
2S
a
=
2 · 106.2
15
= 14.16
hb =
2S
b
=
2 · 106.2
14.17
= 14.99