This is the answer, I hope you didn't need to show work
Answer:
The value of x is 12.1
Step-by-step explanation:
To find the value of x, we will just apply the formula of trigonometric ratio;
SOH CAH TOA
sin Ф = opposite/ hypotenuse
cos Ф = adjacent / hypotenuse
tan Ф = opposite / adjacent
From the diagram given, since we are working with angle 48 then opposite is 9 and hypotenuse is x
Ф =48° opposite = 9 and hypotenuse = x
The best formula to use is;
sin Ф = opposite/ hypotenuse
sin 48° = 
cross-multiply
x sin 48° = 9
Divide both-side by sin 48°
x sin 48° / sin 48° = 9/sin48°
x = 9/sin 48°
=12.11069
x ≈12.1 to the nearest tenth
Therefore the value of x is 12.1
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Since the triangle is a right-angled triangle, we can use SohCahToa to find x
Using the ratio

Opposite = 4ft
adjacent = x
Substituting these values yield

To find Z we use the fact that the sum of angles in a triangle is 180 degrees
so that in triangle XYZ
90 + 25 +Z = 180
Z = 180 - 115
Z= 65 degrees
We will now use Pythagoras theorem to find y
![\begin{gathered} \text{For that} \\ y^2=x^2+4^2 \\ \text{but x = 8.58ft} \\ y^2=8.58^2+4^2 \\ y=\sqrt[]{73.6164\text{ +16}} \\ y\text{ =9.46 ft} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BFor%20that%7D%20%5C%5C%20y%5E2%3Dx%5E2%2B4%5E2%20%5C%5C%20%5Ctext%7Bbut%20x%20%3D%208.58ft%7D%20%5C%5C%20y%5E2%3D8.58%5E2%2B4%5E2%20%5C%5C%20y%3D%5Csqrt%5B%5D%7B73.6164%5Ctext%7B%20%2B16%7D%7D%20%5C%5C%20y%5Ctext%7B%20%3D9.46%20ft%7D%20%5Cend%7Bgathered%7D)
Hence x= 8.58 ft, y= 9.46ft and Z = 65 degrees, Option C