# The horizantol distance between two poles is 15 cm. The angle of depression of the top of first pole as seen from the top of second pole is 30$^{o}$. If the height of the second pole is 24 cm, find the height of the first pole. [use $\pi =\frac{22}{7}$] .

**Given: **The horizontal distance between two poles is$=15\ cm$

The angle of depression of the top of first pole as seen from the top of second pole is $30^{o}$. The height of the second pole is 24 cm

**What to do: **To find the height of the first pole.

**Solution:**

Let AB and CD be the two poles,

height of the first pole=24m

Let us say the height of first pole $AB=h$

Distance between the two poles, $BD = 15\ m$

$AL= BD = 15 m\ and\ AB=DL=h , CL = CD-DL$

$\vartriangle CAL$,

$tan30^{o}=\frac{CL}{AL}$

$\Rightarrow \frac{1}{\sqrt{3}} =\frac{24-h}{15}$

$\Rightarrow 24-h=\frac{15}{\sqrt{3}}$

$\Rightarrow h=24-\ \frac{15}{\sqrt{3}}$

$\Rightarrow h=24-5\sqrt{3}$

$\Rightarrow h=24-5\times 1.732$

$h=15.34\ m$

$\therefore$ The height of second pole is 15.34 m.

Related Articles

- The horizontal distance between two poles is \( 15 \mathrm{~m} \). The angle of depression of the top of the first pole as seen from the top of the second pole is \( 30^{\circ} \). If the height of the second pole is \( 24 \mathrm{~m} \), find the height of the first pole. \( (\sqrt{3}=1.732) \quad \)
- The horizontal distance between two trees of different heights is \( 60 \mathrm{~m} \). The angle of depression of the top of the first tree when seen from the top of the second tree is \( 45^{\circ} \). If the height of the second tree is \( 80 \mathrm{~m} \), find the height of the first tree.
- From the top of a \( 50 \mathrm{~m} \) high tower, the angles of depression of the top and bottom of a pole are observed to be \( 45^{\circ} \) and \( 60^{\circ} \) respectively. Find the height of the pole..
- The ratio of the heights of two boys is 7:6 . if the height of the first boy is 210 cm, what is the height of the second boy
- A circus artist is climbing a $20\ m$ long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is $30^o$ (see figure)."
- A flag pole $18\ m$ high casts a shadow $9.6\ m$ long. Find the distance of the top of the pole from the far end of the shadow.
- A circus artist is climbing a \( 20 \mathrm{~m} \) long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is \( 30^{\circ} \).
- A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that $1\ cm^3$ of iron has approximately 8 g mass. (Use $\pi = 3.14$)
- The length of the shadow of an electric pole in the evening is ____ a) Greater than the length of the electric pole b) Smaller than the length of the electric pole c) Same as the length of the electric pole d) Double the length of the electric pole
- An electric pole is \( 10 \mathrm{~m} \) high. A steel wire tied to top of the pole is affixed at a point on the ground to keep the pole up right. If the wire makes an angle of \( 45^{\circ} \) with the horizontal through the foot of the pole, find the length of the wire.
- On a horizontal plane there is a vertical tower with a flag pole on the top of the tower. At a point 9 metres away from the foot of the tower the angle of elevation of the top and bottom of the flag pole are \( 60^{\circ} \) and \( 30^{\circ} \) respectively. Find the height of the tower and the flag pole mounted on it.
- A flag pole \( 18 \mathrm{~m} \) high casts a shadow \( 9.6 \mathrm{~m} \) long. Find the distance of the top of the pole from the far end of the shadow.
- A pole of height 3 meters is struck by a sledding car and breaks into two pieces such that the first piece is $\frac{1}{2}$ of the second. Find the length of both pieces.
- 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.

##### Kickstart Your Career

Get certified by completing the course

Get Started