The length of the shadow of a tree 8m high, when the sun's elevation is 45⁰ , is .......

1

(a)

8m

If the height of a tower and the distance of the point of observation from its foot, both are increased by 10% then the angle of elevation of its top remains.........

1

(a)

unchanged

The height of a tower is 10m.The height of its shadow when sun's altitude is 45⁰ , is ...........

1

(a)

10m

A 6m tall tree casts a shadow of length 4m.If at the same time  a flagpole casts a shadow 50m in length, then the length of the flagpole is...........

1

(a)

75m

If the ratio of the length of a pole and its shadow is 1 : 1, then angle of elevation of the sun is.......... .

1

(a)

45⁰

If height of a tower and the distance of the point of observation from its foot, both are increased by 20%, then angle of elevation of its remains unchanged

1

(a) False

(b) True

If a man standing on a platform 5m 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.

1

(a) True

(b) False

The length of the shadow of a tree 12m high, when sun's elevation is 45⁰, is \(12\sqrt{3}\)m

1

(a) True

(b) False

A tree is broken by the wind, the top struck the ground at an angles of 60⁰ and at a distance of 30m from the root of the tree.Then whole height of the tree is \(30(2+\sqrt{3})m\).

1

(a) False

(b) True

A circus artist is climbing a 20m long rope which is tightly stretched and tied from the top of a vertical pole to the ground.If the angle made by the rope with the ground level is 30⁰, then the height of the pole is 15m

1

(a) True

(b) False

A vertical stick 10m casts a shadow 8m long.At the same time a tower casts a shadow 32m long.Then the height of the tower is

1

(a)

40m

The angle of elevation of the top of the tower from a point on the ground which is 30m away from foot of the tower is 30⁰.the height of the tower is.

1

(a)

\(10\sqrt{3}m\)

A boy flying a kite has let out 60m of string if the angle of elevation of the kite is 60⁰ , then the height of the kite above the ground is

1

(a)

52m

A girl of height 100cm stands in front of lamppost and cast a shadow of length \(100\sqrt{3}\)cm on the ground.The angle of elevation of the top of the lamppost is 

1

(a)

30⁰

A player sitting on the top of a tower of height 40m observes the angle of depression of a ball lying on the ground as 60⁰.The distance between the foot of the tower and ball is

1

(a)

\({40\over\sqrt{3}}m\)

The angle of elevation of the top of a tower from a point 20 meters away from the base is 45^o . Find the height of the tower.

1

(a)

Let AB is the tower and C is the point 20 m away from the base of the tower 
∴ BC = 20m, ∠ACB = 45^o

In right ΔABC, tan 45^o = \(\frac{AB}{BC}\)
⇒ I = \(\frac{AB}{20}\) ∴ AB = 20 m

If two towers of height h₁ and h₂ subtends angles of 60^o and 30^o respectively at the mid points of line joining their feet, find h₁ : h ₂

1

(a)

Let AB and CD are towers of height h₁ and h₂ respectively 
If F. is the midpoint of BD then BE = DE = x 
In right \(\Delta\)ABE
\(\frac { { h }_{ 1 } }{ x } =\tan { { 60 }^{ o } } \)
\(\Rightarrow\) \({ h }_{ 1 }=\sqrt { 3 } x\)  ...(i)
In right  \(\Delta\)CDE
\(\frac { { h }_{ 2 } }{ x } =\tan { { 30 }^{ o } } \Rightarrow { h }_{ 2 }=\frac { x }{ \sqrt { 3 } } \)
Now \(\frac { { h }_{ 1 } }{ { h }_{ 2 } } =\frac { \sqrt { 3 } x }{ \frac { x }{ \sqrt { 3 } } } =\frac { 3 }{ 1 } \)  \(\Rightarrow\) h₁ : h₂ = 3 : 1

Find the angle of elevation of the top of 15 m high tower at a point 15 m away from the base of the tower.

1

(a)

Let AB is the tower, AB = 15 m, BC = 15 m 
In right \(\Delta\)ABC,  \(\tan { \theta =\frac { AB }{ BC } } \Rightarrow \tan { \theta } =\frac { 15 }{ 15 } \)
\(\Rightarrow\) \(\tan { \theta } =1 \Rightarrow \theta ={ 45 }^{ o }\)

If the elevation of the sun at a given time is 30^o , then find the length of the shadow cast by a tower of 150 feet height at that time.

1

(a)

In right \(\Delta\)ABC
\(\frac { AB }{ BC } =\tan { { 30 }^{ o } } \)
\(\Rightarrow\)  \(\frac { 150 }{ BC } =\frac { 1 }{ \sqrt { 3 } } \)
\(\Rightarrow\)  BC = 150\(\sqrt { 3 } \) feet

At some time of the day the length of the shadow of a tower is equal to its height. Find the sun's altitude at that time.

1

(a)

In right \(\Delta ABC\)
\(tan\theta =\frac { AB }{ BC } \) 
\(\Rightarrow tan\theta =1 \left( \because AB=BC \right) \) 
\(\Rightarrow \theta ={ 45 }^{ o }\)