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.
Given: 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 $30^o$.
To do: To find the distance between the two towers.
Solution:
Let the distance between the two towers$=AB=x\ m$ and height of the other tower$=PA=h\ m$
Given that height of the tower$=QB=30\ m$ and $\angle QAB=60^o,\ \angle PBA=30^o$
Now, in $\vartriangle QAB$,
$\ tan60^o=\frac{QB}{AB}=\frac{30}{x}$
$\Rightarrow \sqrt{3}=\frac{30}{x}$
$\Rightarrow x=\frac{30}{\sqrt{3}}.\frac{\sqrt{3}}{\sqrt{3}}$
$\Rightarrow x=\frac{30\sqrt{3}}{3}=10\sqrt{3}\ m$
Thus, the distance between the towers is $10\sqrt{3}\ m$.
Related Articles
- 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 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 the building from the foot of the tower is \( 30^{\circ} \) and the angle of the top of the tower from the foot of the building is \( 60^{\circ} \). If the tower is \( 50 \mathrm{~m} \) high, find the height of the building.
- 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.
- The angle of elevation of the top of a hill at the foot of a tower is \( 60^{\circ} \) and the angle of elevation of the top of the tower from the foot of the hill is \( 30^{\circ} \). If the tower is \( 50 \mathrm{~m} \) high, what is the height of the hill?
- 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.
- The angle of elevation of the top of tower, from the point on the ground and at a distance of 30 m from its foot, is 30o. Find the height of 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.
- 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 the top of a tower is $30^o$. If the height of the tower is doubled, then check, whether the angle of elevation of its top would double or not.
- The angle of the elevation of the top of vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 30°. Find the height of the tower.
- 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 \( \sqrt{3}=1.732 \) ).
- 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."
- A tower stands vertically on the ground. From a point on the ground, \( 20 \mathrm{~m} \) away from the foot of the tower, the angle of elevation of the top of the tower is \( 60^{\circ} \). What is the height of the tower?
Kickstart Your Career
Get certified by completing the course
Get Started