Horizontal Level and Line of Sight

Q. The angles of depression of the top and bottom of 8 m tall building from the top of a multistoried building are 30° and 45° respectively. Find the height of the multistoried building and the distance between the two buildings.

Q. A pole stands in a park such that its shadow increases by 2 m when the angle of elevation of Sun changes from 45º to 30º. The height of the pole is

1. $(\sqrt{3}-1)m$
2. $2\sqrt{3}m$
3. $(\sqrt{3}+1)m$
4. $\sqrt{3}m$

Q.

The angle of elevation of a jet plane from a point $A$ on the ground is ${60}^{\circ }$. After a flight of $15$ seconds the angle of elevation changes to ${30}^{\circ }$. The plane is flying at a constant height of $1500\sqrt{3}m$. Calculate the speed of the plane.

1. $200m/s$

2. $215m/s$

3. $250m/s$

4. $234m/s$

Q. A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is ${60}^{\circ }$. When he moves 30 metres away from the bank, he finds the angle of elevation to be ${30}^{\circ }$. Find the height of the tree and the width of the river. [Take $\sqrt{3}=1.732$] [4 MARKS]

Q. 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?

Q. Question 15
A vertical pole of a length 6 m casts a shadow 4m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Q.

A man observes the angle of elevation of the top of a building to be 30^o. He walks towards it in a horizontal line through its base. On covering 60 m the ∠ of elevation changes to 60^o. Find the height of the building correct to the nearest metre.

1. 52 m

2. 51 m

3. 26 m

4. 36 m

5. 50 m

Q.

Two lamp posts are of equal height. A boy standing mid-way between then observes the elevation of the top of either post to be ${30}^{\circ }$. After walking $15m$ towards one of them, he observes the elevation of it stop to be ${60}^{\circ }$. Find the heights of the posts and the distance between them.

1. $48m$

2. $45m$

3. $55m$

4. $63m$

Q.

If the shadow of a tower is equal to its height, then the angle of elevation of the top of the tower is ___.

1. 30°

2. 45°

3. 60°

4. 90°

Q. What is the line drawn from the eye of the observer to the the object viewed by the observer?

1. Line of sight
2. Transversal line
3. Horizontal line
4. Vertical line

Q. In figure, a tower AB is 20 m high and BC, its shadow in the ground, is $20\sqrt{3}$ m long. Find the sun's altitude.

Q. The horizontal distance between two towers is 60 metres. The angle of depression of the top of the first tower when seen from the top of the second tower is 30°. If the height of the second tower is 90 metres, find the height of the first tower.$\left[\mathrm{Use}\sqrt{3}=1.732\right]$

Q.

The horizontal distance between two towers is 140 m. The angle of elevation of the top of the first tower when seen from the top of the second tower is 30^o. If the height of the second tower is 60 m then, the height of the first tower is

1. 135 m

2. 142

3. 140.83 m

4. 139.5 m

Q. If the shadow of a building is 27 m when the Sun’s altitude is 30º, then the length of the shadow when the Sun’s altitude is 60º, is

1. 6 m
2. 9 m
3. 15 m
4. 27 m

Q.

A vertical pole & a vertical tower are on the same level ground. From the top of the pole the angle of elevation of the top of the tower is 60^o & the angle of depression of the foot of the tower is 30^o. Find the height of the tower if the height of the pole is 20 m.

1. 80 m

2. 60 m

3. 40 m

4. 70 m

5. 50 m

Q.

From the top of a tower $50m$ high 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.

1. $12.14m$

2. $31.12m$

3. $23.15m$

4. $21.12m$

Q. From a point P on the ground the angle of elevation of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flag-staff from P is 45°. Find the length of the flag-staff and the distance of the building from the point P. (Take $\sqrt{3}=1.732$).

Q.

The shadow of a vertical tower on a level ground increases by 10m when the altitude of the sun changes from 45^o to 30^o. Find the height of the tower, correct to two decimal places.

1. 10.59 m

2. 13.66 m

3. 15.32 m

4. 13.45 m

5. 14.37 m

Q. Two men are on opposite sides of a tower. they measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 metres, find the distance between the two men. $\left[\mathrm{Take}\sqrt{3}=1.732\right]$

Q.

A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 45^o. The height of the tree is:

1. 4.5 m

2. 3 m

3. 4 m

4. 5.2 m

Q. From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30°. From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the distance between the tower and building.

Q. A straight highway leads to the foot of a tower of height 50 m. From the top of the tower, the angles of depression of two cars standing on the highway are 30° and 60° respectively. What is the distance the two cars and how far is each car from the tower?

Q. An observer, $2m$ tall is $10\sqrt{3}m$ away from a tower. The angle of elevation from his eye to the top of the tower is ${30}^{\circ }$. What is the height of the tower?

1. $12m$
2. $14m$
3. $10m$
4. $15m$

Q. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower.
[Use $\sqrt{3}$ = 1.732] [CBSE 2011]

Q.

A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is ${30}^{\circ }$.

1. 5 m

2. 15$\sqrt{3}$ m

3. 18 m

4. 20 m

Q. The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is

(a) $\frac{d}{cot\alpha +cot\beta }$

(b) $\frac{d}{cot\alpha -cot\beta }$

(c) $\frac{d}{\tan \beta -\tan \alpha }$

(d) $\frac{d}{\tan \beta +\tan \alpha }$

Q.

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:

1. 75√3

2. 25√3

3. 150

4. 50√3

Q.

From the top of a building 20 m high, the angle of elevation of the top of a monument is 45° and the angle of depression of its foot is 15°. Find the height of the monument.

1. 94.64 m

2. 93.23 m

3. 89.64 m

4. 78.34 m

Q.

A hot-air balloon is floating above a straight road.

To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon.

The angles of depression are found to be ${20}^{\circ }$ and ${22}^{\circ }.$

How high is the balloon?

Q.

A vertical tower is 20 m high. A man standing at some distance from the tower knows that the cosine of a angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower?

1. 10.25 m

2. 25 m

3. 15 m

4. 5.75 m

5. 12.50 m