Angle of Depression

Q.

The angle of elevation of a cloud from a point 60 m above a lake is ${30}^{\circ }$ and the angle of depression of the reflection of cloud in the lake is ${60}^{\circ }$. Find the height of the cloud.

Q. In triangle ABC, given below, AB = 8 cm, BC = 6 cm and AC= 3 cm. Calculate the length of OC.

Q.

If the angles of elevation of a tower from two points at a distance a and b (where, b>a) from its foot and lying on the same side are ${60}^{\circ }$ and ${30}^{\circ }$, then height of the tower is

1. $\sqrt{ab}$

2. $\sqrt{a-b}$

3. $\sqrt{b-a}$

4. $\sqrt{\frac{a}{b}}$

Q.

State whether the given statement is true or false:

The angle of elevation is the angle between the line of sight of an observer and the horizontal, when the object is below the observer's horizontal line of sight.

1. True

2. False

Q.

The angles of depression of the top and the bottom of a 10 m tall building from the top of a multi-storeyed building are ${30}^{\circ }$ and ${45}^{\circ }$, respectively. Find the distance between the two buildings.

1. 5($\sqrt{3}$ + 3) m

2. 10 m

3. 15 m

4. 5 m

Q. A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from ${60}^{\circ }to{45}^{\circ }$. Calculate the speed of the boat.

Q.

State whether the given statement is true or false:

The angle of depression is the angle between the line of sight of an observer and the object below his horizontal line of sight.

1. False

2. True

Q.

On the two side of a lighthouse, two boats are sailing on the sea. At a particular instant the angle of elevation of the top of the lighthouse as observed from the boats are $60°$ and $45°$ respectively. If the height of the light use is 20m, the distance between the two boats is

1. $\frac{20}{\sqrt{3}}m$

2. $\frac{20(\sqrt{3}+1)}{\sqrt{3}}m$

3. $\frac{(\sqrt{3}+1)}{20\sqrt{3}}m$

4. $\frac{(\sqrt{3}-1)}{20}m$

Q. When the sun's altitude changes from ${30}^{\circ }$ to ${60}^{\circ }$, the length of the shadow of a tower decreases by $70m$. What is the height of the tower?

Q.

State whether the given statement is true or false:

The angle of depression is the angle between the line of sight of an observer and the horizontal, when the object is below the observer's horizontal line of sight.

1. True

2. False

Q.

A vertical stick 10 cm long casts a shadow 8 cm long. At the same time, a tower casts a shadow 30 cm long. Determine the height of the tower?

1. 65 cm

2. 75 cm

3. 37.5 cm

4. 100 cm

Q.

The angle of depression will be :

1. ${120}^{\circ }$

2. None of these

3. ${30}^{\circ }$

4. ${60}^{\circ }$

Q.

The angle of elevation of a cloud from a point $60m$ above a lake is $30°$ and the angle of depression of the reflection of the cloud in the lake is $60°$ find the height of the cloud from the surface of the lake?

Q. A 1.8 m tall man is standing at some distance from a building. The angle of elevation from his eyes to the top of the building increases from ${30}^{\circ }$ to ${60}^{\circ }$ as he walks 20 m towards the building. Find the height of the building (in m). [Take $\sqrt{3}=1.7$]

1. 18.8

Q. A 6 feet tall man sees an apple on the ground, $6\sqrt{3}$ feet away from him. What is the angle of depression when he is looking at the apple?

1. ${60}^{\circ }$
2. $ca{n}^{\prime }tbedetermined$
3. ${30}^{\circ }$
4. ${45}^{\circ }$

Q. A man rowing a boat away from a lighthouse which is 100m high takes 2 mins to change the angle of elevation of the lighthouse from ${60}^{\circ }to{45}^{\circ }$. Calculate the speed of the boat.

Q.
A flagpost casts a 16.8m shadow. At the same time 2.4m shadow is cast by a person who is 1.8m tall. Find the height of the flagpost.

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 __.

Q. A lamp post $5\sqrt{3}$ m high casts a shadow 5 long on the ground. The Sun's elevation at this point is

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q.

The shadow of a tower is three times as long as the shadow of the tower when the suns rays met the ground at an angle of $60°$. Find the angle of elevation of the sun at the time of the long shadow.