Determining the height of a hill from angles of elevation

Question

A surveyor measured the angle of elevation to the top of a hill as 31 degrees. From another point 100 m further away, the angle of elevation was 27 degrees. The surveyor's height was 179 cm. Find the height of the hill. What assumption have you made when determining your solution? Picture and steps below.

I have tried to answer this using algebra with the substitution in method but kept getting a negative number. I check the equation many times but could not find any issues. I tried searching online for an answer but could not find any. Thanks for any help.

https://i.stack.imgur.com/JDj8Q.png

Edited

Answer 1

You made a mistake when doing the $-y$ in the first step.

You should've, instead, done $y\tan(31 º)=(100+y)\tan(27º)$.

This is because from $y$ meters away, the angle is $31º$, and from $100+y$ meters away, the angle is $27º$.

And then, once you find the height (in meters), you can add on $179$ cm, or $1.79$m.

Answer 2

Hint:

Here is a close example. Remember that you still need to add the survior's height to the final height calculated.

Source: Tree Height - Wikipedia