I don’t know where I found this question, but it does require algebra and problem solving (as well as right trig and Pythagoras)
From a point 
, a lighthouse is on a bearing of 
T and the top of the light house is at an angle of elevation of 
. From a point 
, the lighthouse is on a bearing of 
T and the top of the lighthouse is at angle of elevation of 
. If and are 500 metres apart, find the height of the lighthouse.
Let’s draw a diagram.
Let the height of the lighthouse be 
We can find the angle between , the lighthouse, and by using the base triangle
The red line from 
is parallel to the two north lines. Hence 
(Alternate angles in parallel lines are congruent)
It’s a right triangle so we know
(1) 
We are going to use the other two triangles to find 
and 
   |    |
Substitute and into equation 
Solve for .
