Can somebody help me, please? I just need help with #12
the first attachment is supposed to help and the second attachment has the question I need to be answered. Please show your work

 x = 9.6

Explanation:

We have two smaller right triangles that are glued together so to speak.

The base of the smaller triangle on the left is 5 while the height is h.

Let's use the tangent rule to find the value of h

tan(angle) = opposite/adjacent

tan(55) = h/5

5*tan(55) = h

h = 5*tan(55)

h = 7.14074003371058

Make sure your calculator is in degree mode. That value of h above is approximate.

Now focus on the smaller triangle on the right

It has the same height value h. This side is the adjacent side while x is the hypotenuse.

We'll use the cosine ratio

cos(angle) = adjacent/hypotenuse

cos(42) = h/x

cos(42) = 7.14074003371058/x

x*cos(42) = 7.14074003371058

x = 7.14074003371058/cos(42)

x = 9.6088135029715

x = 9.6