Question

The angle of elevation of the top of a building from the foot of the tower is 300 and

the angle of elevation of the top of the tower from the foot of the bulding is 600 . If the

tower is 30m high,find the height of the building​

Answer 1

Correct Question:-

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 30m high, find the height of the building.

Given:-

• Angle of elevation of the top of a building from the foot of the tower = 30°
• Angle of elevation of the top of the tower from the foot of the building = 60°
• Height of tower = 30m

To find:-

• The height of the building.

Note:-

• Refer to the attachment for the diagram.

Solution:-

Here we can see that there are two right-angled triangles.

For ∆CBA,

∠CAB = 30°

BC = 30 m

We know,

TanA = $\sf{\dfrac{Perpendicular}{Base}}$

Hence,

Tan30° = $\sf{\dfrac{BC}{AB}}$

From trigonometric table we have,

Tan30° = $\sf{\dfrac{1}{\sqrt{3}}}$

Hence,

$\sf{\dfrac{1}{\sqrt{3}} = \dfrac{30}{AB}}$

$\sf{\implies AB = 30\sqrt{3}\longrightarrow[i]}$

Now,

For ∆DAB,

∠DBA = 60°

Now,

Tan60° = $\sf{\dfrac{AD}{AB}}$

From trigonometric table we have,

Tan60° = √3

Hence,

$\sf{\sqrt{3} = \dfrac{AD}{AB}}$

Putting the value of AB from equation [i]

$\sf{\sqrt{3} = \dfrac{AD}{30\sqrt{3}}}$

$\sf{\implies \sqrt{3}\times 30\sqrt{3} = AD}$

$\sf{\implies 30\times 3 = AD}$

$\sf{\implies AD = 90\:m}$

Hence, The height of the building is 90 m.

______________________________________

Trigonometric Table:-

$Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$