From a point $P$, a person observes that the angle of elevation of the top of a cliff $A$ is $40°$. After walking $100$ m towards $A$ along a straight road inclined upwards at an angle of $15°$ to the horizontal, the angle of elevation of $A$ is observed to be $50°$. Find the vertical height of $A$ above $P$.
I really need help with this question. I keep getting $219.8$m when the answers say $212.3$m. There is no working out in the solutions.
The diagram i used can be accessed here: https://drive.google.com/file/d/1Su59ZXg_QfAc_p8xceDBw5da0kKqeetn/view?usp=sharing
You made a mistake in your diagram. In your diagram, you are supposed to mark $x_1$ as $100$m and not the base in the right triangle that also has side $y$ opposite angle $15^{\circ}$. Using this correction and your diagram the vertical height ($h$) should be (in meters): $$h=100\left(\sin 15^{\circ} + \frac{\sin 25^{\circ} \sin 50 ^{\circ}}{\sin 10^{\circ}}\right) \approx 212.3$$