Question

Help please on this question

Answer 1

To find x, first, we have to calculate the second leg of the bigger triangle using Pythagorean's Theorem.

`\begin{gathered} 18^2=12^2+z^2 \\ z=\sqrt[]{324-144} \\ z=\sqrt[]{180}\approx13.4 \end{gathered}`

Then, we find the acute angle in the triangle on the right.

`\begin{gathered} \tan \theta=(12)/(18) \\ \theta=\tan ^(-1)((12)/(18))\approx34 \end{gathered}`

Now, using this angle, we find the other part that sums 18 with x.

`\begin{gathered} \cos \theta=(y)/(13.4) \\ y=13.4\cdot\cos 34\approx11 \end{gathered}`

Then, we subtract to find x

`x=18-11=7`Hence, x = 7.