В треугольнике со сторонами: a = 4, b = 2, с = 4.628, углы равны α° = 59.5°, β° = 25.5°, γ° = 95°
Ответ:
a=4
b=2
c=4.628
α°=59.5°
β°=25.5°
γ°=95°
S = 3.984
ha=1.992
hb=3.984
hc=1.722
P = 10.63
Решение:
Угол:
γ° = 180 - α° - β°
= 180 - 59.5° - 25.5°
= 95°
Высота :
hc = a·sin(β°)
= 4·sin(25.5°)
= 4·0.4305
= 1.722
Сторона:
c = √a2 + b2 - 2ab·cos(γ°)
= √42 + 22 - 2·4·2·cos(95°)
= √16 + 4 - 16·-0.08716
= √21.39
= 4.625
или:
c = a·
sin(γ°)
sin(α°)
= 4·
sin(95°)
sin(59.5°)
= 4·
0.9962
0.8616
= 4·1.156
= 4.624
или:
c = b·
sin(γ°)
sin(β°)
= 2·
sin(95°)
sin(25.5°)
= 2·
0.9962
0.4305
= 2·2.314
= 4.628
Периметр:
P = a + b + c
= 4 + 2 + 4.628
= 10.63
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√5.314·(5.314-4)·(5.314-2)·(5.314-4.628)
=√5.314 · 1.314 · 3.314 · 0.686
=√15.874261676784
= 3.984
Высота :
ha =
2S
a
=
2 · 3.984
4
= 1.992
hb =
2S
b
=
2 · 3.984
2
= 3.984