В треугольнике со сторонами: a = 877.72, b = 1250, с = 890, углы равны α° = 44.6°, β° = 90°, γ° = 45.4°
Ответ:
a=877.72
b=1250
c=890
α°=44.6°
β°=90°
γ°=45.4°
S = 390645.8
ha=890.14
hb=625.03
hc=877.86
P = 3017.7
Решение:
Угол:
γ° = arcsin(
c
b
sin(α°))
= arcsin(
890
1250
sin(90°))
= arcsin(0.712·1)
= 45.4°
Угол:
α° = 180 - γ° - β°
= 180 - 45.4° - 90°
= 44.6°
Сторона:
a = √b2 + c2 - 2bc·cos(α°)
= √12502 + 8902 - 2·1250·890·cos(44.6°)
= √1562500 + 792100 - 2225000·0.712
= √770400
= 877.72
или:
a = b·
sin(α°)
sin(β°)
= 1250·
sin(44.6°)
sin(90°)
= 1250·
0.7022
1
= 1250·0.7022
= 877.75
или:
a = c·
sin(α°)
sin(γ°)
= 890·
sin(44.6°)
sin(45.4°)
= 890·
0.7022
0.712
= 890·0.9862
= 877.72
Периметр:
P = a + b + c
= 877.72 + 1250 + 890
= 3017.7
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√1508.9·(1508.9-877.72)·(1508.9-1250)·(1508.9-890)
=√1508.9 · 631.18 · 258.9 · 618.9
=√152604106609.34
= 390645.8
Высота :
ha =
2S
a
=
2 · 390645.8
877.72
= 890.14
hb =
2S
b
=
2 · 390645.8
1250
= 625.03
hc =
2S
c
=
2 · 390645.8
890
= 877.86