Question

A person observes the top and foot of a Cell Tower within the angle of elevation of

60° and angle of depression 30° respectively. From the top of building of height 10 M.

Draw a diagram to find the height of the Cell Tower​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• AB represents the building.

• CD represents the Cell Tower.

Now, it is given that

• AB = 10 m

Now, from the top of building B, the angle of elevation of top of Cell building D is 60°.

and

From the top of building B, the angle of depression of foot of cell tower C is 30°.

Construction : Draw BE perpendicular to CD meeting CD at E.

Let assume that DE = 'x' m and BE = AC = 'y' m.

Now,

In triangle BED,

$\rm :\longmapsto\:tan60 \degree \: = \: \dfrac{ED}{BE}$

$\rm :\longmapsto\: \sqrt{3} = \dfrac{x}{y}$

$\bf\implies \:x = \sqrt{3}y - - - (1)$

Now,

In triangle BEC

$\rm :\longmapsto\:tan30 \degree \: = \: \dfrac{EC}{BE}$

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} } = \dfrac{10}{y}$

$\bf\implies \:y = 10 \sqrt{3} \: m$

Substituting the value of y in equation (1) we get

$\bf\implies \:x = \sqrt{3} \times 10 \sqrt{3} = 30 \: m$

Hence,

The height of Cell Tower = CD = x + 10 = 30 +10 = 40 m.

Additional Information :-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$