Answer:
The height of tower [tex]DB=111\ meters[/tex].
Step-by-step explanation:
Diagram of the given scenario is shown below.
Given that,
Distance between John and tower is [tex]CE=150 \ meters[/tex].
Angle of elevation to the top of the tower is [tex]\angle DEC=36[/tex]°.
Height of John is [tex]CB=2\ meters[/tex].
To Find: Height of the tower [tex]DB[/tex].
So,
In triangle ΔDCE,
[tex]Tan[/tex](∠[tex]DEC)= \frac{DC}{CE}[/tex]
[tex]Tan (36)= \frac{DC}{150}[/tex]
[tex]DC= tan(36)\times 150[/tex]
[tex]DC=108.98\ meters[/tex]
Now,
To calculate the height of tower we have
[tex]DB=DC+CB[/tex]
[tex]DB=108.98+2[/tex]
[tex]DB=110.98\ meters[/tex] ≈ [tex]111 \ meters[/tex]
Therefore,
The height of tower [tex]DB=111\ meters[/tex].
