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Published on: 27/08/2019
Some Applications of Trigonometry
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1.
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
2.
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
3.
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
4.
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.
5.
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
6.
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.
7.
If the elevation of the sun at a given time is 30o , then find the length of the shadow cast by a tower of 150 feet height at that time.
8.
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.
9.
If two towers of height h1 and h2 subtends angles of 60o and 30o respectively at the mid points of line joining their feet, find h1 : h 2
10.
The angle of elevation of the top of a tower from a point 20 meters away from the base is 45o . Find the height of the tower.
11.
If the ratio of the length of a pole and its shadow is 1 : 1, then angle of elevation of the sun is.......... .
12.
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...........
13.
The height of a tower is 10m.The height of its shadow when sun's altitude is 450 , is ...........
14.
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.........
15.
The length of the shadow of a tree 8m high, when the sun's elevation is 450 , is .......
16.
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
17.
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 \(30(2+\sqrt{3})m\).
18.
The length of the shadow of a tree 12m high, when sun's elevation is 450, is \(12\sqrt{3}\)m
19.
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.
20.
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.
\({40\over\sqrt{3}}m\)
2.
300
3.
52m
4.
\(10\sqrt{3}m\)
5.
40m
6.
In right \(\Delta ABC\)
\(tan\theta =\frac { AB }{ BC } \)
\(\Rightarrow tan\theta =1 \left( \because AB=BC \right) \)
\(\Rightarrow \theta ={ 45 }^{ o }\)
7.
In right \(\Delta\)ABC
\(\frac { AB }{ BC } =\tan { { 30 }^{ o } } \)
\(\Rightarrow\) \(\frac { 150 }{ BC } =\frac { 1 }{ \sqrt { 3 } } \)
\(\Rightarrow\) BC = 150\(\sqrt { 3 } \) feet
8.
Let AB is the tower, AB = 15 m, BC = 15 m
In right \(\Delta\)ABC, \(\tan { \theta =\frac { AB }{ BC } } \Rightarrow \tan { \theta } =\frac { 15 }{ 15 } \)
\(\Rightarrow\) \(\tan { \theta } =1 \Rightarrow \theta ={ 45 }^{ o }\)
9.
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
10.
Let AB is the tower and C is the point 20 m away from the base of the tower
∴ BC = 20m, ∠ACB = 45o
In right ΔABC, tan 45o = \(\frac{AB}{BC}\)
⇒ I = \(\frac{AB}{20}\) ∴ AB = 20 m
11.
( )
450
12.
( )
75m
13.
( )
10m
14.
( )
unchanged
15.
( )
8m
16.
(b)
17.
(a)
18.
(b)
19.
(b)
20.
(a)
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