An illustration of the given situation is shown below:
In order to determine the height x of the tower, take into account that the opposite side to angle 75° is (x - 1.63). Then, by using the tangent of 75°, you have:
[tex]\tan 75=\frac{\text{opposite}}{\text{adjacent}}=\frac{x-1.63}{36.37}[/tex]By solving for x and simplifying, you obtain:
[tex]\begin{gathered} 36.37\cdot\tan 75=x-1.63 \\ x=36.37\cdot\tan 75+1.63 \\ x\approx137.36 \end{gathered}[/tex]Hence, you can conclude that the height of the tower is approximately 137.36m
