В треугольнике со сторонами: a = 95, b = 95, с = 49.18, углы равны α° = 75°, β° = 75.02°, γ° = 30°
Ответ:
a=95
b=95
c=49.18
α°=75°
β°=75.02°
γ°=30°
S = 2256.4
ha=47.5
hb=47.5
hc=91.76
P = 239.18
Решение:
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √952 + 952 - 2·95·95·cos(30°)
= √9025 + 9025 - 18050·0.866
= √2418.7
= 49.18
Угол:
α° = arcsin(
a
c
sin(γ°))
= arcsin(
95
49.18
sin(30°))
= arcsin(1.932·0.5)
= 75.02°
или:
α° = arccos(
b2+c2-a2
2bc
)
= arccos(
952+49.182-952
2·95·49.18
)
= arccos(
9025+2418.6724-9025
9344.2
)
= 75°
Угол:
β° = arcsin(
b
c
sin(γ°))
= arcsin(
95
49.18
sin(30°))
= arcsin(1.932·0.5)
= 75.02°
Периметр:
P = a + b + c
= 95 + 95 + 49.18
= 239.18
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√119.59·(119.59-95)·(119.59-95)·(119.59-49.18)
=√119.59 · 24.59 · 24.59 · 70.41
=√5091506.0913424
= 2256.4
Высота :
ha =
2S
a
=
2 · 2256.4
95
= 47.5
hb =
2S
b
=
2 · 2256.4
95
= 47.5
hc =
2S
c
=
2 · 2256.4
49.18
= 91.76