В треугольнике со сторонами: a = 15, b = 17, с = 8.998, углы равны α° = 61.72°, β° = 86.34°, γ° = 31.89°
Ответ:
a=15
b=17
c=8.998
α°=61.72°
β°=86.34°
γ°=31.89°
S = 67.37
ha=8.983
hb=7.926
hc=14.97
P = 41
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √152 + 172 - 2·15·17·cos(31.89°)
= √225 + 289 - 510·0.8491
= √80.96
= 8.998
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
15
8.998
sin(31.89°))
= arcsin(1.667·0.5283)
= 61.72°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
172+8.9982-152
2·17·8.998
)
= arccos(
289+80.964004-225
305.93
)
= 61.72°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
17
8.998
sin(31.89°))
= arcsin(1.889·0.5283)
= 86.34°
Периметр:
P = a + b + c
= 15 + 17 + 8.998
= 41
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√20.5·(20.5-15)·(20.5-17)·(20.5-8.998)
=√20.5 · 5.5 · 3.5 · 11.502
=√4538.97675
= 67.37
Высота :
ha =
2S
a
=
2 · 67.37
15
= 8.983
hb =
2S
b
=
2 · 67.37
17
= 7.926
hc =
2S
c
=
2 · 67.37
8.998
= 14.97