STEP 1: Identify and Set Up
We are given a triangle that is divided into two right angled triangles. Our approach is to find the side opposite 43 degrees since it is the same side adjacent to 32 degrees then find x subsequently. We will use the SOH CAH TOA method to evaluate the problem.
We have two triangles and we'll draw them separately to aid understanding.
STEP 2: Execute
Our first goal is to find the length of y. We can use the SOH
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypothenuse}=\sin 43=\frac{y}{39}\text{ | Observe the initials} \\ \text{Therefore,} \\ y=39\sin 43=26.6 \end{gathered}[/tex]
We can now apply this value of y to solve x in our other triangle. We use TOA
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}\text{ | Observe the initials} \\ \tan 32=\frac{x}{y}=\frac{x}{26.6} \\ \text{Therefore,} \\ x=26.6\tan 32=16.6 \end{gathered}[/tex]
x = 16.6
