2 2/5 servings of cake
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Answer:
The length of XY is either 10 or 2.5.
Step-by-step explanation:
Given information: ZY = 5, XC = 3 and DC = 4.
Case 1: Rectangle ABCD is smaller than ZBXY.
The opposite sides of the rectangle are same.
![ZY=BC+XC](https://tex.z-dn.net/?f=ZY%3DBC%2BXC)
![5=BC+3](https://tex.z-dn.net/?f=5%3DBC%2B3)
![2=BC](https://tex.z-dn.net/?f=2%3DBC)
The length of ABCD is 4 and width of ABCD is 2. The width of ZBXY is 5. The corresponding sides of the similar rectangles are is in the same proportion.
![\frac{4}{XY}=\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7BXY%7D%3D%5Cfrac%7B2%7D%7B5%7D)
![\frac{4\times 5}{2}=XY](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Ctimes%205%7D%7B2%7D%3DXY)
![10=XY](https://tex.z-dn.net/?f=10%3DXY)
Therefore the value of XY is 10.
Case 2: Rectangle ABCD is larger than ZBXY.
![ZY=BC-XC](https://tex.z-dn.net/?f=ZY%3DBC-XC)
![5=BC-3](https://tex.z-dn.net/?f=5%3DBC-3)
![8=BC](https://tex.z-dn.net/?f=8%3DBC)
The length of ABCD is 4 and width of ABCD is 8. The width of ZBXY is 5. The corresponding sides of the similar rectangles are is in the same proportion.
![\frac{4}{XY}=\frac{8}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7BXY%7D%3D%5Cfrac%7B8%7D%7B5%7D)
![\frac{4\times 5}{8}=XY](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Ctimes%205%7D%7B8%7D%3DXY)
![2.5=XY](https://tex.z-dn.net/?f=2.5%3DXY)
Therefore the value of XY is 2.5.
The answer is the last option
Which is (49x-16)^2
The tangent ratio is
tan(38°) = opposite/adjacent = (height of cliff)/(distance to base)
Multiplying the equation by the denominator gives
height of cliff = (80 ft)*tan(38°) ≈ 62.5 ft