The shadow of a tower standing on a level plane is found to be $50\ m$ longer. When Sun's elevation $30^o$ than when it is $60^o$. Find the height of tower.
Given: The shadow of a tower standing on a level plane is found to be $50\ m$ longer, when Sun's elevation $30^o$ than when it is $60^o$
To do: To find the height of tower.
Solution:
$tan60^o=\frac{h}{BC}$
$BC=\frac{h}{\sqrt{3}}\ ........\ ( i)$
$tan30^o=\frac{h}{BC+50}$
$\Rightarrow BC+50=\sqrt{3}h$
$BC=\sqrt{3}h−50\ .......\ ( ii)$
From $( i)$ & $( ii)$
$\frac{h}{\sqrt{3}}=\sqrt{3}h-50$
$\Rightarrow h=3h−50\sqrt{3}$
$\Rightarrow 2h=50\sqrt{3}$
$\Rightarrow h=25\sqrt{3}$
Related Articles
- The shadow of a tower standing on a level ground is found to be $40\ m$ longer when the Sun's altitude is $30^{\circ}$ than when it is $60^{\circ}$. Find the height of the tower.
- The shadow of a tower standing on a level ground is found to be \( 40 \mathrm{~m} \) longer when Sun's altitude is \( 30^{\circ} \) than when it was \( 60^{\circ} \). Find the height of the tower.
- The shadow of a tower, when the angle of elevation of the sun is \( 45^{\circ} \), is found to be \( 10 \mathrm{~m} \). longer than when it was \( 60^{\circ} \). Find the height of the tower.
- The length of the shadow of a tower standing on level plane is found to be \( 2 x \) metres longer when the sun's altitude is \( 30^{\circ} \) than when it was \( 45^{\circ} \). Prove that the height of tower is \( x(\sqrt{3}+1) \) metres.
- The length of shadow of a tower on the play-ground is square root three times the height of the tower. The angle of elevation of the sun is: $( A) \ 45^{o}$$( B) \ 30^{o}$$( C) \ 60^{o}$$( D) \ 90^{o}$
- The angle of elevation of the top of a tower from a point on the ground, which is $30\ m$ away from the foot of the tower is $30^o$. Find the height of the tower.
- The angle of elevation of the top of a building from the foot of a tower is $30^o$ and the angle of elevation of the top of the tower from the foot of the building is $60^o$. If the tower is $50\ m$ high, find the height of the building.
- From the top of a 7 m high building, the angle of the elevation of the top of a tower is $60^{o}$ and the angle of the depression of the foot of the tower is $30^{o}$. Find the height of the tower.
- The angle of elevation of the top of a tower $30\ m$ high from the foot of another tower in the same plane is $60^o$ and the angle of elevation of the top of the second tower from the foot of the first tower is $30^o$. then find the distance between the two towers.
- A person observed the angle of elevation of the top of a tower as \( 30^{\circ} \). He walked \( 50 \mathrm{~m} \) towards the foot of the tower along level ground and found the angle of elevation of the top of the tower as \( 60^{\circ} \). Find the height of the tower.
- The angle of elevation of top of tower from certain point is $30^o$. if the observer moves $20\ m$ towards the tower, the angle of elevation of the top increases by $15^o$. Find the height of the tower.
- From the top of a building \( 15 \mathrm{~m} \) high the angle of elevation of the top of a tower is found to be \( 30^{\circ} \). From the bottom of the same building, the angle of elevation of the top of the tower is found to be \( 60^{\circ} \). Find the height of the tower and the distance between the tower and building.
- From the top of a $7\ m$ high building, the angle of elevation of the top of a cable tower is $60^o$ and the angle of depression of its foot is $45^o$. Determine the height of the tower.
- A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^o$. From another point $20\ m$ away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^o$ (see the given figure). Find the height of the tower and the width of the canal."
- The angle of elevation of a tower from a point on the same level as the foot of the tower is \( 30^{\circ} \). On advancing 150 metres towards the foot of the tower, the angle of elevation of the tower becomes \( 60^{\circ} \). Show that the height of the tower is \( 129.9 \) metres (Use \( \sqrt{3}=1.732 \) ).
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies