Finding path difference of EM waves received by radio telecopes

[songoku]

Homework Statement

Please see below

Relevant Equations

Trigonometry

My attempt:

I think $x$ is the path difference so by using trigonometry, I got $x=d \sin \theta$

But my teacher said the answer is $d \cos \theta$

What is my mistake? Thanks

Edit: Sorry, I found my mistake. My $x$ is not the path difference

 

[BvU]

OK, well done.

Tip: Always check a result for extreme cases (like here: $\theta = 0$ and $\theta = \pi/2$)

$\$

 

[haruspex]

My x is not the path difference

Well, it is the difference between the path lines, but not the path length difference.

 

[songoku]

Thank you very much BvU and haruspex