Angle of Elevation

Q.

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. If the lighthouse is $100m$ high, the distance between the two ships is:

Take $\sqrt{3}=1.73$

1. $300m$

2. $200m$

3. $273m$

4. $173m$

Q.

The angle of elevation of a ladder leaning against a wall is ${60}^{\circ }$ and the foot of the ladder is 9.5m away from the wall. Find the length of the ladder.

Q.

The angle of elevation of a stationery cloud from a point 2500 m above a lake is ${15}^{\circ }$ and the angle of depression of its reflection in the lake is ${45}^{\circ }$. What is the height of the cloud above the lake level? (Use tan ${15}^{\circ }$ = 0.268)

Q. Question 1
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 ${30}^{\circ }$.

Q.

The angle of elevation of the top of a tower from a point A on the ground is ${30}^{\circ }$. On moving a distance of 20 metres towards the foot of the tower to a point B the angle of elevation increases to ${60}^{\circ }$. Find the height of the tower and the distance of the tower from the point A.

Q.

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of ${60}^{\circ }$. After 10 seconds, its elevation is observed to be ${30}^{\circ }$. Find the speed of the aeroplane in km/hr.

Q. Question 8
Find the angle of elevation of the Sun when the shadow of a pole "h" m high is "$\sqrt{3}$ h" m long.

Q.

The angle of elevation of the top of a vertical tower from a point on the ground is ${60}^{\circ }$. From another point 10 m vertically above the first, its angle of elevation is ${30}^{\circ }$ . Find the height of the tower.

Q. A spherical balloon of radius 4 cm subtends an angle 60º at the eye of an observer. If the angle of elevation of its centre is 45º, then the height of the centre of the balloon is

1. $\sqrt{2}cm$
2. $\sqrt{3}cm$
3. $4\sqrt{2}cm$
4. $2\sqrt{3}cm$

Q.

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 ${30}^{\circ }$ [1 MARK]

Q.

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of ${60}^{\circ }$ with the wall, then find the height of the wall.

Q.

If the height of a vertical pole is $\sqrt{3}$ times the length of its shadow on the ground then the angle of elevation of the sun at that time is

(a) ${30}^{\circ }$

(b) ${45}^{\circ }$

(c) ${60}^{\circ }$

(d) ${75}^{\circ }$

Q. What is the angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree?

1. ${60}^{\circ }$
2. ${45}^{\circ }$
3. ${80}^{\circ }$
4. ${90}^{\circ }$

Q.

If the length of the shadow of a tower is $\sqrt{3}$ times its height then the angle of elevation of the sun is

(a) ${45}^{\circ }$

(b) ${30}^{\circ }$

(c) ${60}^{\circ }$

(d) ${90}^{\circ }$

Q.

The angle of elevation of the top of a tower from a point on the ground, which is $30m$ away from the foot of the tower, is $30°$. Find the height of the tower.

Q. Question 13
The angle of elevation of the top of a tower 30m high from the foot of another tower in the same plane is ${60}^{\circ }$ and the angle of elevation of the top of the second tower from the foot of the first tower is ${30}^{\circ }$. Find the distance between the two towers and also the height of the tower.

Q. At a point A, 20 m above the level of water in a lake, the angle of elevation of a cloud is ${30}^{\circ }$. The angle of elevation of the reflection of the cloud in the lake, at A is ${60}^{\circ }$. Find the distance of the cloud from A.

Q. The angle of elevation of the sun is , when the length of the shadow of a tree is equal to the height of the tree.

1. ${60}^{\circ }$
2. ${45}^{\circ }$
3. ${30}^{\circ }$

Q. The angles of elevation of a balloon from the observer’s eye at two instances are 45º and 60º. If the height of balloon in both the instants is 10 m and it takes $(\sqrt{3}-1)$ seconds, then the approximate speed of the balloon is $(\text{Use}\sqrt{3}=1.73)$

1. 4.8 m/s
2. 5 m/s
3. 6.4 m/s
4. 5.8 m/s

Q.

If the height of a vertical pole is equal to the length of its shadow on the ground, the angle of elevation of the sun is

(a) $0^{\circ }$

(b) ${30}^{\circ }$

(c) ${45}^{\circ }$

(d) ${60}^{\circ }$

Q.

Find the angle of elevation of the sum (sun's altitude) when the length of the shadow of a vertical pole is equal to its height

Q. Question 7
Write ‘True’ or ‘False’ and justify your answer in each of the following:
If the length of the shadow of a tower is increasing, then the angle of elevation of the Sun is also increasing.

Q. A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?

1. $15(2\sqrt{5}-5)m$
2. $15(3\sqrt{3}-2)m$
3. $15(2\sqrt{3}-3)m$
4. $15(2\sqrt{2}-2)m$

Q.

An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is ${60}^{\circ }$. Find the height of the chimney.

Q.

The angles of elevation of the top of a rock from the top and foot of a 100 m high tower are respectively ${30}^{\circ }$ and ${45}^{\circ }$ . Find the height of the rock.

Q.

From the top of a cliff 25m high, the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is:

1. 25m

2. 75m

3. 50m

4. 100m

Q.

Find the angular elevation of the sun when the shadow of a 10 m long pole is $10\sqrt{3}m.$

1. ${15}^{\circ }$

2. ${30}^{\circ }$

3. ${60}^{\circ }$

4. ${45}^{\circ }$

Q. Question 3
The angle of elevation of the top of a tower from a certain point is ${30}^{\circ }$. If the observer moves 20m towards the tower, the angle of elevation of the top increases by ${15}^{\circ }$. Find the height of the tower.

Q. Question 17
A window of a house is h m above the ground. Form the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be $\alpha$ and $\beta$, respectively. Prove that the height of the other house is $h(1+tan\alpha cot\beta )m$.

Q. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of ${30}^{\circ }$. A girl standing on the roof of a 20-m-high building finds the angle of elevation of the same bird to be ${45}^{\circ }$. The boy and the girl are on the opposite sides of the bird. Find the distance of the bird from the girl. [Given $\sqrt{2}=1.41$] [4 MARKS]