The answer is exactly £5,472
The slope is positive. Hope this helps :)
Answer:
![\displaystyle \tan(\theta)=-\frac{\sqrt{17}}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%28%5Ctheta%29%3D-%5Cfrac%7B%5Csqrt%7B17%7D%7D%7B8%7D)
Step-by-step explanation:
We are given that:
![\displaystyle \cos(\theta)=\frac{8}{9}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ccos%28%5Ctheta%29%3D%5Cfrac%7B8%7D%7B9%7D)
Where θ is in QIV.
And we want to find the value of tan(θ).
Recall that cosine is the ratio of the adjacent side over the hypotenuse.
Therefore, the opposite side is:
![o=\sqrt{9^2-8^2}=\sqrt{17}](https://tex.z-dn.net/?f=o%3D%5Csqrt%7B9%5E2-8%5E2%7D%3D%5Csqrt%7B17%7D)
Next, in QIV, only cosine is positive: sine and tangent are both negative.
Tangent is the ratio of the opposite side to the adjacent. So:
![\displaystyle \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%28%5Ctheta%29%3D%5Cfrac%7B%5Ctext%7Bopposite%7D%7D%7B%5Ctext%7Badjacent%7D%7D)
Substitute. Tangent is negative in QIV. Hence:
![\displaystyle \tan(\theta)=-\frac{\sqrt{17}}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%28%5Ctheta%29%3D-%5Cfrac%7B%5Csqrt%7B17%7D%7D%7B8%7D)