Trigonometric problem: Elevation angle The elevation of the top of a tower $KT$ from a point $A$ is $27^\circ$. At another point $B$, $50$ meters nearer to the foot of the tower where $ABK$ is a straight line, the angle of elevation is $40^\circ$. Find the height of the tower $KT$.

Consider the following diagram:

Looking at the outer (right-angled) triangle ($TAK$), and using trigonometry, we have:
$$(1) \tan(27)=\frac{h}{50+x}.$$
Looking at the inner (right-angled) triangle ($TBK$), and using trigonometry, we have:
$$(2) \tan(40)=\frac{h}{x}.$$
Now we've got a pair of simultaneous equations, $(1)$ and $(2)$. Solve them!
Also bear in mind that $\tan(27)$ and $\tan(40)$ are just numbers which you can find on a calculator.
