Question

John stands 150 meters from a water tower and sights the top at an angle of elevation of 36º. If John's eyes are 2 meters above the ground, how tall is the tower? Round to the nearest meter.

Answer 1

Answer:

The height of tower $DB=111\ meters$.

Step-by-step explanation:

Diagram of the given scenario is shown below.

Given that,

Distance between John and tower is  $CE=150 \ meters$.

Angle of elevation to the top of the tower is $\angle DEC=36$°.

Height of John is  $CB=2\ meters$.

To Find: Height of the tower $DB$.

So,

In triangle ΔDCE,

                    $Tan$(∠$DEC)= \frac{DC}{CE}$

                    $Tan (36)= \frac{DC}{150}$

                     $DC= tan(36)\times 150$

                     $DC=108.98\ meters$

Now,

To calculate the height of tower we have

                    $DB=DC+CB$

                    $DB=108.98+2$

                    $DB=110.98\ meters$ ≈ $111 \ meters$

Therefore,

The height of tower $DB=111\ meters$.