Question

The picture shows a triangular island:Which expression shows the value of z? x sin 50°y/cos 50° x cos 50°y/sin 50°

Answer 1

In order to find an expression for z, we can use the sine and cosine relations of the angle 50°.

The sine is equal to the opposite leg over the hypotenuse, and the cosine is equal to the adjacent leg over the hypotenuse.

So we have:

$\begin{gathered} \sin50°=\frac{x}{z}\\ \\ z=\frac{x}{\sin50°}\\ \\ \\ \\ \cos50°=\frac{y}{z}\\ \\ z=\frac{y}{\cos50°} \end{gathered}$

Therefore the correct option is the second one.