В треугольнике со сторонами: a = 8.799, b = 32.84, с = 34, углы равны α° = 15°, β° = 75°, γ° = 90°
Ответ:
a=8.799
b=32.84
c=34
α°=15°
β°=75°
γ°=90°
S = 144.5
ha=32.84
hb=8.8
hc=8.499
P = 75.64
Решение:
Сторона:
a = c·
sin(α°)
sin(γ°)
= 34·
sin(15°)
sin(90°)
= 34·
0.2588
1
= 34·0.2588
= 8.799
Угол:
β° = 180 - γ° - α°
= 180 - 90° - 15°
= 75°
Сторона:
b = √a2 + c2 - 2ac·cos(β°)
= √8.7992 + 342 - 2·8.799·34·cos(75°)
= √77.42 + 1156 - 598.33·0.2588
= √1078.6
= 32.84
или:
b = a·
sin(β°)
sin(α°)
= 8.799·
sin(75°)
sin(15°)
= 8.799·
0.9659
0.2588
= 8.799·3.732
= 32.84
или:
b = c·
sin(β°)
sin(γ°)
= 34·
sin(75°)
sin(90°)
= 34·
0.9659
1
= 34·0.9659
= 32.84
Высота :
hc = a·sin(β°)
= 8.799·sin(75°)
= 8.799·0.9659
= 8.499
Периметр:
P = a + b + c
= 8.799 + 32.84 + 34
= 75.64
Площадь:
p =
a + b + c
2
S =√p·(p-a)·(p-b)·(p-c)
=√37.82·(37.82-8.799)·(37.82-32.84)·(37.82-34)
=√37.82 · 29.021 · 4.98 · 3.82
=√20879.812931592
= 144.5
Высота :
ha =
2S
a
=
2 · 144.5
8.799
= 32.84
hb =
2S
b
=
2 · 144.5
32.84
= 8.8