Answer:
Proved: ![c\sin A=a\sin C\Rightarrow \frac{\sin A}{a}=\frac{\sin C}{c}](https://tex.z-dn.net/?f=c%5Csin%20A%3Da%5Csin%20C%5CRightarrow%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D)
Step-by-step explanation:
Given: A triangle
To prove: ![\frac{\sin A}{a}=\frac{\sin C}{c}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D)
Solution:
Trigonometry is a branch of mathematics that explains relationship between sides and angles of the triangle.
Sine of angle = side opposite to the angle / hypotenuse
In ΔADB,
![\sin A=\frac{BD}{AB}=\frac{h}{c}\\\Rightarrow h=c\sin A\,\,\,(i)](https://tex.z-dn.net/?f=%5Csin%20A%3D%5Cfrac%7BBD%7D%7BAB%7D%3D%5Cfrac%7Bh%7D%7Bc%7D%5C%5C%5CRightarrow%20h%3Dc%5Csin%20A%5C%2C%5C%2C%5C%2C%28i%29)
In ΔBDC,
![\sin C=\frac{BD}{BC}=\frac{h}{a}\\\Rightarrow h=a\sin C\,\,\,(ii)](https://tex.z-dn.net/?f=%5Csin%20C%3D%5Cfrac%7BBD%7D%7BBC%7D%3D%5Cfrac%7Bh%7D%7Ba%7D%5C%5C%5CRightarrow%20h%3Da%5Csin%20C%5C%2C%5C%2C%5C%2C%28ii%29)
From equations (i) and (ii),
![c\sin A=a\sin C\\\frac{\sin A}{a}=\frac{\sin C}{c}](https://tex.z-dn.net/?f=c%5Csin%20A%3Da%5Csin%20C%5C%5C%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%3D%5Cfrac%7B%5Csin%20C%7D%7Bc%7D)
Hence proved
Answer:
x = 8
y = 14
Step-by-step explanation:
2x + 6 = 4x - 10 (Corresponding angles so they're equal)
2x - 4x = -10 - 6
-2x = -16
x = 8
2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)
2(8) + 6 + 13y - 24 = 180
16 + 6 + 13y - 24 = 180
13y - 2 = 180
13y = 182
y = 14
Answer:
I think the slope is -20/17 hope this helps
The percent decrease between 9.74 and 9.65 is ≈0.92%decrease