Question

A boy 1.7 m tall is 25 m away from a tower and observes the angle of elevation of the top of the tower to be \[{{60}^{\circ }}\]. Find the height of the tower.
A. 55 m
B. 45 m
C. 20 m
D. 35 m

Answer 1

Hint: Firstly draw a clear diagram of this situation with angle of elevation. Equate the boy’s height with the tower and assume the rest of the height. Use \[\vartriangle ABC\] this to write \[\tan {{60}^{\circ }}=\dfrac{h}{25}\]. After putting the value we have to just calculate the rest of the sum. After getting the value of assumed height we have to add it with the height of the boy. After this addition we can get the height of the tower.

Complete step by step solution:
First of all let's draw a diagram where everything is visible according to the question.

In the diagram CD is the boy who is 1.7m tall. He can observe the angle of elevation of the top of the tower to be \[\angle ACB={{60}^{\circ }}\].
According to the diagram CD=BE=1.7m
Let us assume that AB= h
So the height of the tower is,
\[\left( h+1.7 \right)\]m
The distance between boy and tower is given in the question which is DE=BC=25m.
From \[\vartriangle ABC\] we can write,
\[\tan {{60}^{\circ }}=\dfrac{h}{25}\]
Putting the value of \[\tan {{60}^{\circ }}=\sqrt{3}\] we get,
\[\begin{align}
  & \sqrt{3}=\dfrac{h}{25} \\
 & \Rightarrow h=25\sqrt{3} \\
\end{align}\]
After putting the value of \[\sqrt{3}=1.732\] we get,
\[\begin{align}
  & \Rightarrow h=25\times 1.732 \\
 & \Rightarrow h=43.301 \\
\end{align}\]

From the value of h we can calculate the height of the tower.
So the height of the tower is,
\[\left( h+1.7 \right)\]
\[\Rightarrow \left( 43.301+1.7 \right)\]
\[\Rightarrow 45\]
Height of the tower is 45m (Option B).

Note: Students have to understand the angle of elevation. Students have to remember the value of \[\sqrt{3}=1.732\]. They get confused by the value of \[\tan {{60}^{\circ }}=\sqrt{3}\] with the value of \[\tan {{30}^{\circ }}=\dfrac{1}{\sqrt{3}}\]. So they have to remember these values. For height and distance questions, students forget to draw diagrams. But it is necessary to draw diagrams for these kinds of problems.