# 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 ?

**Given:** Height of the tower$=30\ m$ length of the shadow$=10\sqrt{3} m\ $

**To do:** To find the angle of the elevation of the sun.

**Solution:**

Angle of equation of sun$=\angle GST=\theta $

Height of lower $TG=30\ m$

Length of shadow $GS\ =10\sqrt{3} \ m$

$\vartriangle TGS$ is a right angled triangle,

$\therefore tan\theta =\frac{30}{10\sqrt{3}} =\frac{3}{\sqrt{3}} =\sqrt{3}$

As known $tan60^{o}=\sqrt{3}$

$\therefore \ \theta =60^{o}$

Thus the angle of the elevation is $60^{o}$

- Related Articles
- 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.
- 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
- 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"\n
- 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$
- If the length of the shadow of a tower is increasing, then find the changes in the angle of elevation of the sun.
- 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 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.
- An observer, \( 1.5 \mathrm{~m} \) tall, is \( 28.5 \mathrm{~m} \) away from a tower \( 30 \mathrm{~m} \) high. Determine the angle of elevation of the top of the tower from his eye.
- 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 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.
- 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.

##### Kickstart Your Career

Get certified by completing the course

Get Started