Hello, daydreembelievr!

Your diagram is wrong . . .

From a point on ground level, the angle of elevation to the top of a mountain is 35°.

160 m farther away from the mountain, the angle of elevation is 15º.

Find the height of the mountain. Code:

P *
| * *
| * *
h| * *
| * *
| 35° * 15° *
* - - - - - * - - - - - - - - *
Q x A 160 B

The height of the mountain is: $\displaystyle h = PQ.$

The first observation is made at $\displaystyle A\!:\;\;x = QA,\;\angle PAQ = 35^o$

The second observation is made at $\displaystyle B\!:\;\;AB = 160,\;\angle PBQ = 15^o$

In right triangle $\displaystyle PQB\!:\;\;\tan15^o \:=\:\frac{h}{x+160} \quad\Rightarrow\quad x \:=\:\frac{h}{\tan15^o} - 160$ .[1]

In right triangle $\displaystyle PQA\!:\;\;\tan35^o \:=\:\frac{h}{x}\quad\Rightarrow\quad x \:=\:\frac{h}{\tan35^o} $ .[2]

Equate [1] and [2]: . $\displaystyle \frac{h}{\tan15^o}-160 \:=\:\frac{h}{\tan35^o} \quad\hdots\quad \text{and solve for }h$