# In the following figure, a tower AB is $20\ m$ high and BC, its shadow on the ground, is $20\sqrt{3} \ m$ long. Find the Sun's altitude.br"

**Given:** Height of the tower, $AB=20\ m$ and its shadow on the ground, BC=20$\sqrt{3}$m.

**To do: **To find the sun's altitude.

**Solution:**

Let AB be the tower and BC be its shadow and $\theta $ be the sun's altitude.

$AB = 20,\ BC = 20$, $\theta=?$

In $\vartriangle ABC$,

$tan\theta=\frac{AB}{BC} \ \ \ \ \ \ \ \ \ \ \ \ ( \because tan\theta =\frac{perp.}{base})$

$\Rightarrow tan\theta =\frac{20}{20\sqrt{3}}$

$\Rightarrow tan\theta =\frac{1}{\sqrt{3}}$

But as known $tan30^{o}=\frac{1}{\sqrt{3}}$

$\Rightarrow tan\theta =tan30^{o}$

$\Rightarrow \theta =30^{o}$

The sun's altitude is at $30^{o}$.

- Related Articles
- If a tower $30\ m$ high, casts a shadow $10\sqrt{3} \ m$ long on the ground, then what is the angle of elevation of the sun ?
- If a pole $6\ m$ high casts a shadow $2\sqrt{3}\ m$ long on the ground, then find the sun’s elevation.
- A pole \( 6 \mathrm{~m} \) high casts a shadow \( 2 \sqrt{3} \mathrm{~m} \) long on the ground, then the Sun's elevation is(A) \( 60^{\circ} \)(B) \( 45^{\circ} \)(C) \( 30^{\circ} \)(D) \( 90^{\circ} \)
- A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
- A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow \( 28 \mathrm{~m} \) long. Find the height of the tower.
- A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow \( 28 \mathrm{~m} \) long. Fin the height of the tower.
- The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is $30^{o}$ .The distance of the car from the base of the tower $( in\ m)$ is:$( A) \ 25\sqrt{3}$$( B) \ 50\sqrt{3}$$( C) \ 75\sqrt{3}$$( D) \ 150$
- 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?
- A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 m long. Determine the height of the tower."\n
- An electric pole casts a shadow of length 20 m at a time when a tree 6 m high casts a shadow of length 8 m. Find the height of the pole.
- From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a $20\ m$ high building are $45^o$ and $60^o$ respectively. Find the height of the tower.
- From a point on the ground the angles of elevation of the bottom and top of a transmission tower fixed at the top of \( 20 \mathrm{~m} \) high building are \( 45^{\circ} \) and \( 60^{\circ} \) respectively. Find the height of the transimission tower.
- A stone resting on the ground has a gravitational force of 20 N acting on it. What is the weight of the stone? What is its mass? $(g=10 m/s^2)$.
- 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 stone is dropped from a height of 20 m.(i) How long will it take to reach the ground?(ii) What will be its speed when it hits the ground? $(g=10\ m/s^2)$

##### Kickstart Your Career

Get certified by completing the course

Get Started