Answer
355k+ views
Hint- Draw the diagram of question and use value of trigonometric angles $\tan {30^0} =
\frac{1}{{\sqrt 3 }}$ and $\tan {60^0} = \sqrt 3 $ .
Let QR be the height of the tower (h meters) and RS be the height of flagstaff surmounted on
the tower (RS=5m). Let the point P lie on the horizontal plane at a distance of x meters from
the foot of the tower at point Q (PQ=x meters).
In $\vartriangle PQR$, the angle of elevation of the bottom of the flagstaff is ${30^0}$ .
$
\tan {30^0} = \dfrac{{QR}}{{PQ}} \\
\Rightarrow \dfrac{1}{{\sqrt 3 }} = \frac{h}{x} \\
\Rightarrow x = \sqrt 3 h.........\left( 1 \right) \\
$
In $\vartriangle PQS$, angle of elevation of the top of the flagstaff is ${60^0}$ .
$
\tan {60^0} = \dfrac{{QS}}{{PQ}} = \dfrac{{QR + RS}}{{PQ}} \\
\Rightarrow \sqrt 3 = \dfrac{{h + 5}}{x} \\
\Rightarrow x = \dfrac{{h + 5}}{{\sqrt 3 }}..........\left( 2 \right) \\
$
Eliminating x using (1) and (2) equation
$
\Rightarrow \sqrt 3 h = \dfrac{{h + 5}}{{\sqrt 3 }} \\
\Rightarrow 3h = h + 5 \\
\Rightarrow 2h = 5 \\
\Rightarrow h = 2.5m \\
$
So, the height of tower is 2.5 meters
Note- Whenever we face such types of problems we use some important points. Like draw
the figure of question with notify all points and distances then make the relation between
variables with the help of trigonometric angles then after eliminating x we can get the value
of the height of the tower.
\frac{1}{{\sqrt 3 }}$ and $\tan {60^0} = \sqrt 3 $ .
Let QR be the height of the tower (h meters) and RS be the height of flagstaff surmounted on
the tower (RS=5m). Let the point P lie on the horizontal plane at a distance of x meters from
the foot of the tower at point Q (PQ=x meters).
![seo images](https://www.vedantu.com/question-sets/94399cc2-9378-43cd-96f9-7610f2c359385230471727447006587.png)
In $\vartriangle PQR$, the angle of elevation of the bottom of the flagstaff is ${30^0}$ .
$
\tan {30^0} = \dfrac{{QR}}{{PQ}} \\
\Rightarrow \dfrac{1}{{\sqrt 3 }} = \frac{h}{x} \\
\Rightarrow x = \sqrt 3 h.........\left( 1 \right) \\
$
In $\vartriangle PQS$, angle of elevation of the top of the flagstaff is ${60^0}$ .
$
\tan {60^0} = \dfrac{{QS}}{{PQ}} = \dfrac{{QR + RS}}{{PQ}} \\
\Rightarrow \sqrt 3 = \dfrac{{h + 5}}{x} \\
\Rightarrow x = \dfrac{{h + 5}}{{\sqrt 3 }}..........\left( 2 \right) \\
$
Eliminating x using (1) and (2) equation
$
\Rightarrow \sqrt 3 h = \dfrac{{h + 5}}{{\sqrt 3 }} \\
\Rightarrow 3h = h + 5 \\
\Rightarrow 2h = 5 \\
\Rightarrow h = 2.5m \\
$
So, the height of tower is 2.5 meters
Note- Whenever we face such types of problems we use some important points. Like draw
the figure of question with notify all points and distances then make the relation between
variables with the help of trigonometric angles then after eliminating x we can get the value
of the height of the tower.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)