When you have two lines in an x shape, vertical angles are the ones opposite each other.
in the example here, the angles with the purple dots are vertical angles and the angles with the blue dots are the other vertical angles
The difference in the volume of the 2 wardrobes is that she wants a new wardrobe that is a foot wider than her last wardrobe.
Answer:
width: 7 cm
length: 56 cm
Step-by-step explanation:
Let:
x=width
8x=length
P=2l+2w
126=2x + 2(8x)
126=2x+16x
18x=126
x=7
width: 7 cm
length: 56 cm
hope this helps!!
Recall that
![\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\pm\sqrt{1-\sin^2\theta}](https://tex.z-dn.net/?f=%5Ccos%5E2%5Ctheta%2B%5Csin%5E2%5Ctheta%3D1%5Cimplies%5Ccos%5Ctheta%3D%5Cpm%5Csqrt%7B1-%5Csin%5E2%5Ctheta%7D)
But we're specifically told that cosine is negative, so we take the negative root above, and then
![\cos\theta=-\sqrt{1-\left(\dfrac34\right)^2}=-\dfrac{\sqrt7}4](https://tex.z-dn.net/?f=%5Ccos%5Ctheta%3D-%5Csqrt%7B1-%5Cleft%28%5Cdfrac34%5Cright%29%5E2%7D%3D-%5Cdfrac%7B%5Csqrt7%7D4)
Now,
![\csc\theta=\dfrac1{\sin\theta}=\dfrac43](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac1%7B%5Csin%5Ctheta%7D%3D%5Cdfrac43)
![\cot\theta=\dfrac{\cos\theta}{\sin\theta}=-\dfrac{\sqrt7}3](https://tex.z-dn.net/?f=%5Ccot%5Ctheta%3D%5Cdfrac%7B%5Ccos%5Ctheta%7D%7B%5Csin%5Ctheta%7D%3D-%5Cdfrac%7B%5Csqrt7%7D3)
3 times 4 is 12. Tack 3 0's to get 12,000.