# A flag post stands on the top of a building. From a point on the ground, the angles of elevation

of the top and the bottom of the flag post are ${60^0}$ and ${45^0}$ respectively. If the height of the flag post is $10m$, find the height of the building. \[\left( {\sqrt 3 = 1.732} \right)\]

Last updated date: 23rd Mar 2023

•

Total views: 307.8k

•

Views today: 6.86k

Answer

Verified

307.8k+ views

Hint: Draw the figure and use trigonometric formulas to solve.

Le A be the point of observation and B be the foot of the building.

Let BC denote the height of the building and CD denote height of the flag post.

Given that \[\angle CAB = {45^ \circ },{\text{ }}\angle DAB = {60^ \circ }{\text{ and }}CD = 10m\]

Let \[BC = h{\text{ metres}}\] and \[AB = x{\text{ metres}}\].

Now in the right angled \[\Delta CAB\],

\[\tan {45^ \circ } = \dfrac{{BC}}{{AB}}\]

Thus, AB =BC i.e. $x = h$ -Equation(1)

Also, in right angled \[\Delta DAB\],

\[

{\text{tan6}}{{\text{0}}^ \circ }{\text{ = }}\dfrac{{BD}}{{AB}} \\

\Rightarrow AB = \dfrac{{h + 10}}{{\tan {{60}^ \circ }}} \\

\]

\[ \Rightarrow {\text{ }}x = \dfrac{{h + 10}}{{\sqrt 3 }}\] -Equation (2)

From Equation (1) and Equation (2) we get,

\[

h = \dfrac{{h + 10}}{{\sqrt 3 }} \\

\Rightarrow \sqrt 3 h - h = 10 \\

\Rightarrow h = \left( {\dfrac{{10}}{{\sqrt 3 - 1}}} \right) \\

\]

Now, when we rationalize it we get,

\[

h = \left( {\dfrac{{10}}{{\sqrt 3 - 1}}} \right)\left( {\dfrac{{\sqrt 3 + 1}}{{\sqrt 3 + 1}}} \right) = \dfrac{{10\left( {\sqrt 3 + 1} \right)}}{{3 - 1}} \\

{\text{ = 5}}\left( {2.732} \right) = 13.66m \\

\]

Hence, the height of the building is \[13.66m\]

Note: In these types of questions it is always necessary to make the figure as described in the question properly as this stage is most prone to error. Then, we use the given angles and lengths and find the desired value using simple trigonometry.

Le A be the point of observation and B be the foot of the building.

Let BC denote the height of the building and CD denote height of the flag post.

Given that \[\angle CAB = {45^ \circ },{\text{ }}\angle DAB = {60^ \circ }{\text{ and }}CD = 10m\]

Let \[BC = h{\text{ metres}}\] and \[AB = x{\text{ metres}}\].

Now in the right angled \[\Delta CAB\],

\[\tan {45^ \circ } = \dfrac{{BC}}{{AB}}\]

Thus, AB =BC i.e. $x = h$ -Equation(1)

Also, in right angled \[\Delta DAB\],

\[

{\text{tan6}}{{\text{0}}^ \circ }{\text{ = }}\dfrac{{BD}}{{AB}} \\

\Rightarrow AB = \dfrac{{h + 10}}{{\tan {{60}^ \circ }}} \\

\]

\[ \Rightarrow {\text{ }}x = \dfrac{{h + 10}}{{\sqrt 3 }}\] -Equation (2)

From Equation (1) and Equation (2) we get,

\[

h = \dfrac{{h + 10}}{{\sqrt 3 }} \\

\Rightarrow \sqrt 3 h - h = 10 \\

\Rightarrow h = \left( {\dfrac{{10}}{{\sqrt 3 - 1}}} \right) \\

\]

Now, when we rationalize it we get,

\[

h = \left( {\dfrac{{10}}{{\sqrt 3 - 1}}} \right)\left( {\dfrac{{\sqrt 3 + 1}}{{\sqrt 3 + 1}}} \right) = \dfrac{{10\left( {\sqrt 3 + 1} \right)}}{{3 - 1}} \\

{\text{ = 5}}\left( {2.732} \right) = 13.66m \\

\]

Hence, the height of the building is \[13.66m\]

Note: In these types of questions it is always necessary to make the figure as described in the question properly as this stage is most prone to error. Then, we use the given angles and lengths and find the desired value using simple trigonometry.

Recently Updated Pages

Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE