Angle of Elevation and Angle of Depression

Q. The angle of elevation of an aeroplane from point A on the ground is ${60}^{\circ }$. After flight of 15 seconds, the angle of elevation change to ${30}^{\circ }$. If the aeroplane is flying at a constant height of $1500\sqrt{3}$ m, find the speed of the plane in km/hr.

Q.

The ratio of the length of a rod and its shadow is 1: √3. The angle of elevation of the sun is

1. 90^o

2. 60^o

3. 45^o

4. 30^o

Q. Question 8
If a man standing on a platform 3m above the surface of a lake observes a cloud and its reflection in the lake, then the angle of elevation of the cloud is equal to the angle of depression of its reflection.

Q.

If the angle of elevation of a cloud from a point 100 metres above a lake is 30^o and the angle of depression of its reflection in the lake is 60^o, then the height of the cloud above the lake is

1. 200 m

2. 30 m

3. 500 m

4. 100 m

Q. A man who is 2 m tall stands on horizontal ground 30 m away from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.
(Use sin 28° = 0.4694, cos 28° = 0.8829, and tan 28° = 0.5371)

1. 5.3 m
2. 17.95 m
3. 7.3 m
4. 10.8 m

Q.

When the sun is at an elevation of ${35}^{\circ }$, the shadow of a tree is 10 m. What would be the length of the shadow, when the sun is at an elevation of ${25}^{\circ }$?

$\left[\begin{array}{c}Tan{25}^{\circ }=0.46\\ Tan{35}^{\circ }=0.7\end{array}\right]$

1. 18.24 m

2. 15.21 m

3. 12.42 m

4. 21.32 m

Q.

One sees the top of a tree on a bank of a river at an elevation of ${70}^{\circ }$ from the other bank. Stepping 20 m back, he sees the top of the tree at an elevation of ${55}^{\circ }$. If height of the person is $1.4m$ then the width of river is $[tan{70}^{\circ }=2.75,tan{55}^{\circ }=1.43]$

1. 26.4 m

2. 21.66 m

3. 28.2 m

4. 25.4 m

Q.

The fig., shows the observation of point C from point A. The angle of depression from A is:

1. 45^o

2. 60^o

3. 30^o

4. 75^o

Q.

Length of shadow of a tree 12m high when Sun's elevation is ${45}^{\circ }$ is $12\sqrt{3}$

1. True

2. False

Q.

Two buildings on a plane ground are 20 m apart. From the top of the smaller building one can see the base of the taller building at an angle of depression of ${50}^{\circ }$ and its top at an angle of elevation of ${25}^{\circ }.$ The height of the bigger building will be $[Tan{50}^{\circ }=1.2Tan{25}^{\circ }=0.46]$

1. 33.3 m

2. 39.3 m

3. 43.6 m

4. 27.3 m

Q.

A tower is built on a river of width 80 m. One can see the top of the tower at an angle of elevation of ${55}^{\circ }$ and ${65}^{\circ }$ from either banks of the river. The height of tower measured from the water level is $[Tan{65}^{\circ }=2.14,Tan{55}^{\circ }=1.43]$

1. 76.2 m

2. 52.4 m

3. 68.57 m

4. 58.3 m

Q.

If the angle of elevation of a cloud from a point 60 m above a lake is 30 and the angle of depression of its reflection in the lake be 60 .find the height of the cloud from the surface of the lake.

Q.

Two buildings on a plane ground are 30 m apart. From the top of the smaller building, one sees the base of the other building at an angle of depression of ${60}^{\circ }$ and its top at an elevation of ${35}^{\circ }.$ The height of the bigger building is

$\left[\begin{array}{c}Tan{60}^{\circ }=1.7\\ Tan{35}^{\circ }=0.7\end{array}\right]$

Let CD $\&$ AB be the smaller and taller building respectively.

DE = AC = 30 m

1. 82 m

2. 52 m

3. 72 m

4. 62 m

Q. ntA straight rod partially immersed in water appears to be inclined at 45 degree with the surface when viewed vertically through air.What is the actual inclination of rod with water?n nta)30 degreen ntb)45 degreen ntc)33 degreen ntd)180 degreen

Q. A boy, standing on a 50 m tall building is looking at a stone on the ground. The distance between the stone and the building is equal to the height of the building. Find the angle of depression.

Q. Which of the following figures illustrates the angle of elevation and the angle of depression from the same point?

1. 
2. 
3. 
4. 

Q.

A person standing at some distance from a tower sees the top of the tower, making an angle of elevation of ${50}^{\circ }$. When he moves 10 m towards the tower the angle of elevation changes to ${70}^{\circ }$. The height of the tower is

$[tan{70}^{\circ }=2.74,tan{50}^{\circ }=1.2]$

1. 28.21 m

2. 14.21 m

3. 21.35 m

4. 22.75 m

Q. Find the angle of elevation of the sun, if a 12 m high electric pole casts a 12 m long shadow.

1. 30 deg
2. 45 deg
3. 60 deg
4. 90 deg

Q.

A security guard standing on the top of a 100 m high lighthouse sees an enemy ship coming towards it. It was initially at an angle of depression of ${35}^{\circ }$ but after 10 minutes the angle of depression changes to ${55}^{\circ }$. The speed of enemy ship is equal to $[tan{55}^{\circ }=1.42,tan{35}^{\circ }=0.7]$

1. 7.9 m / min

2. 8.5 m / min

3. 7.2 m / min

4. 6.6 m / min

Q.

A man watches his friend swimming in his apartment swimming pool from the roof of the building which is 50 m high. When the swimmer was at one end, the angle of depression was ${40}^{\circ }$. When the swimmer reaches the other end, the angle of depression changes to 65${}^{\circ }$. The distance covered by the swimmer is

$[Tan{65}^{\circ }=2.14,Tan{40}^{\circ }=0.83]$

1. 42.54 m

2. 36.88 m

3. 46.78 m

4. 32.94 m

Q. If the object is below the level of the observer, then the angle between the _____ and the observer's line of sight is called the angle of depression.

1. horizontal
2. vertical
3. (a) and (b) above
4. none of the above

Q.

A Person Standing on a boat at point A sees a submarine at point B, making an angle of depression of ${60}^{\circ }$. After sometime, the submarine travels 100 m and moves to point C. Now, the angle of depression becomes 30${}^{\circ }$. Find the distance the boat has to travel to reach a point that is exactly above the submarine. $[Tan{30}^{\circ }=0.57,tan{60}^{\circ }=1.73]$

1. 86.2 m

2. 96.4 m

3. 82.4 m

4. 78.6 m

Q.

Two poles of equal heights are standing opposite each other on either side of the road, which is 90 m wide. From a point between them on the road, the angles of elevation of the top of the poles are ${60}^{\circ }$ and ${30}^{\circ }$, respectively. Find the height of the poles.

Q.

A man rowing a boat away from a lighthouse which is 100 m high takes 2 min to change the angle of elevation of the light house from ${45}^{\circ }$ to ${30}^{\circ }$. The speed of the boat is $[Tan{45}^{\circ }=1,Tan{30}^{\circ }=0.57]$

1. 37.7 m /min

2. 75.4 m /min

3. 26.7 m /min

4. 47.4 m /min

Q.

As observed from the top of a lighthouse, the angles of depression of two ships are ${30}^{\circ }$ and ${45}^{\circ }$. If one ship is exactly behind the other on the same side of the lighthouse and is 100m apart, find the height of the lighthouse from the sea-level.

Q. A man on top of a building observes a car at an angle of depression $\alpha$, where $tan\alpha =\frac{1}{\sqrt{5}}$ and sees that it is moving towards the base of the building. Ten minutes later the angle of depression of the car is found to be $\beta$ where tan $\beta =\sqrt{5}$. If the car is moving with an uniform speed, then how much more time will it take to reach the base of the tower?

Q.

From an aeroplane vertically above a horizontal road, the angles of depression of two friends standing on either side of the aeroplane are observed to be $\alpha \&\beta$. The distance between the two friends is 1 m. The height (in metres) of the aeroplane from the ground is

1. $\frac{Tan\alpha -Tan\beta }{Tan\alpha .Tan\beta }$

2. $\frac{Tan\alpha .Tan\beta }{Tan\alpha +Tan\beta }$

3. $\frac{Tan\alpha .Tan\beta }{Tan\alpha -Tan\beta }$

4. $\frac{Tan\alpha +Tan\beta }{Tan\alpha .Tan\beta }$

Q.

The angle of elevation of a cloud from a point 60 m above a lake is 30⁰ and the angle of depression of the reflection of the cloud in the lake is 60⁰. Find the height of the cloud.

1. 120 m

2. 140 m

3. 230 m

4. 210 m

Q.

If a person is looking down at an object, then the angle the man’s line of sight makes with his eye level is the angle of ___.

1. elevation

2. depression

3. adjacent angle

4. straight angle

Q.

Two towers are 40m apart. The angle of elevation of the top of the taller tower from the base and top of the shorter tower is ${70}^{\circ }$ and ${40}^{\circ }$ respectively. The height of the shorter tower is $[Tan{40}^{\circ }=0.83,Tan{70}^{\circ }=2.74]$

1. 76. 33 m

2. 82.43 m

3. 72.43 m

4. 86.33 m