Triangulation Question

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I am working my way through a book called Trigonometry: A Complete Introduction.

I am stuck on one of the triangulation questions and was wondering of someone could help. The answer is 2.23 km but i don't get anywhere near that answer.

Can someone help?

Excercise 6.3 Q8

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HINT

Perhaps the following figure will help:

enter image description here

Consider that

$$x+y=m\cot(\alpha)+m\cot(\beta)=5.$$

Now, you have $m$. Then $m'$. Then $h$.