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.

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

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

$\begin{gathered} \cos \theta=\frac{y}{13.4} \\ y=13.4\cdot\cos 34\approx11 \end{gathered}$

Then, we subtract to find x

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