# Class 10

Explore popular questions from Some Applications of Trigonometry for Class 10. This collection covers Some Applications of Trigonometry previous year Class 10 questions hand picked by experienced teachers.

## Mathematics

Some Applications of Trigonometry

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Q 1. The angle of elevation of the top of a tower from the top and bottom of a building of height 'a' are {tex} 30 ^ { \circ } {/tex}and {tex} 45 ^ { \circ } {/tex} respectively. If the tower and the building stand at the same level, the height of the tower is.

A

{tex} \mathrm { a } \sqrt { 3 } {/tex}

B

{tex} a ( \sqrt { 3 } - 1 ) {/tex}

{tex} a \frac { ( 3 + \sqrt { 3 } ) } { 2 } {/tex}

D

{tex} a ( \sqrt { 3 } + 1 ) {/tex}

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Q 2. From the top of a light house {tex} 60 \mathrm { mt } {/tex}. high with it's base at sea level, the angle of depression of a boat is {tex} 15 ^ { \circ } . {/tex} The distance of the boat from the foot of the light house is

A

{tex} \left( \frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } \right) 60 \mathrm { mt } {/tex}

{tex} \left( \frac { \sqrt { 3 } + 1 } { \sqrt { 3 } - 1 } \right) 60 \mathrm { mt } {/tex}

C

{tex} \left( \frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 } \right) \mathrm { mt } {/tex}

D

none of these

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Q 3. On level ground the angle of elevation of the top of the tower is {tex} 30 ^ { \circ } . {/tex} On moving {tex} 20 \mathrm { mt } {/tex}. near, then angle of elevation is {tex} 60 ^ { \circ } . {/tex} The height of the tower is

A

{tex} 20 \sqrt { 3 } {/tex}

{tex} 10 \sqrt { 3 } {/tex}

C

{tex} 10 ( \sqrt { 3 } - 1 ) {/tex}

D

none

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Q 4. A pole stand vertically inside a triangular park {tex} \mathrm { ABC } {/tex}. If the angle of elevation of the top of the pole from each corner of the park is same then in {tex} \Delta \mathrm { ABC } {/tex} the foot of the pole is at

A

centriod

circumcentre

C

incentre

D

ortho centre

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Q 5. A pole {tex} 25 \mathrm { m } {/tex}. long stands on the top of a tower {tex} 225 \mathrm { m } {/tex}. high. If '{tex} \theta {/tex}' is the angle subtended by the pole at a point on the ground which is at a distance of {tex} 2.25 \mathrm { km } {/tex} from the foot of the tower, then {tex} \tan \theta {/tex} is equal to

A

{tex} 1 / 90 {/tex}

B

{tex} 1 / 91 {/tex}

C

{tex} 1 / 10 {/tex}

{tex} 1 / 9 {/tex}

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Q 6. A tower stands vertically in a field. The field is in the shape of an equilateral triangle of side {tex} 100 \mathrm { mt } {/tex}. The tower subtend's angles of {tex} 30 ^ { \circ } , 60 ^ { \circ } {/tex} at the vertices of a triangle. Find the height of the tower.

A

{tex} \frac { 50 } { \sqrt { 3 } } \mathrm { mt } {/tex}

{tex} 50 \sqrt { 3 } \mathrm { mt } {/tex}

C

{tex} \frac { 25 } { \sqrt { 3 } } \mathrm { mt } {/tex}

D

{tex} 25 \sqrt { 3 } \mathrm { mt } {/tex}

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Q 7. Match the following (one to one)
Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. Only One entries of column-I may have the matching with the same entries of column- II and one entry of column-II Only one matching with entries of column-I

{tex} (A)- ( \mathrm { R } ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { P } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { Q } ) {/tex}

D

{tex} ( \mathrm { D } ) - ( \mathrm { S } ) {/tex}

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Q 8. A pole {tex} 6 \mathrm { m } {/tex} high casts a shadow {tex} 2 \sqrt { 3 } \mathrm { m } {/tex} long on the ground, then the Sun's elevation is :

{tex} 60 ^ { \circ } {/tex}

B

{tex} 45 ^ { \circ } {/tex}

C

{tex} 30 ^ { \circ } {/tex}

D

{tex} 90 ^ { \circ } {/tex}

##### Explanation

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Q 9. The angle of depression of a car parked on the road from the top of {tex} 150 \mathrm { m } {/tex} high tower is {tex} 30 ^ { \circ } . {/tex} The distance of the car from the tower (in metres) is :

A

{tex} 50 \sqrt { 3 } {/tex}

{tex} 150 \sqrt { 3 } {/tex}

C

{tex} 150 \sqrt { 2 } {/tex}

D

{tex} 75{/tex}

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Q 10. The length of a string between a kite and a point on the ground is {tex} 85 \mathrm { m } {/tex}. If the string makes an angle {tex} \theta {/tex} with the ground level such that tan {tex} \theta = \frac { 15 } { 8 } , {/tex} then the kite is at what height from the ground?

{tex} 75 \mathrm { m } {/tex}

B

{tex} 79.41 \mathrm { m } {/tex}

C

{tex} 80 \mathrm { m } {/tex}

D

{tex} 72.5 \mathrm { m } {/tex}

##### Explanation

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Q 11. If the height of a vertical pole is {tex} \sqrt { 3 } {/tex} times the length of its shadow on the ground, then the angle of elevation of the Sun at that time is :

A

{tex} 30 ^ { \circ } {/tex}

{tex} 60 ^ { \circ } {/tex}

C

{tex} 45 ^ { \circ } {/tex}

D

{tex} 75{/tex}

##### Explanation

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Q 12. The angle of depression of a car, standing on the ground, from the top of a {tex} 75 \mathrm { m } {/tex} high tower, is {tex} 30 ^ { \circ } . {/tex} The distance of the car from the base of the tower (in {tex} \mathrm { m. } {/tex} ) is :

A

{tex} 25 \sqrt { 3 } {/tex}

B

{tex} 50 \sqrt { 3 } {/tex}

{tex} 75 \sqrt { 3 } {/tex}

D

{tex} 150{/tex}

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Q 13. From the top of a cliff {tex} 20 \mathrm { m } {/tex} high, the angle of elevation of the top 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 :

A

{tex} 20 \mathrm { m } {/tex}

{tex} 40 \mathrm { m } {/tex}

C

{tex} 60 \mathrm { m } {/tex}

D

{tex} 80 \mathrm { m } {/tex}

##### Explanation

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Q 14. The ratio of the length of a rod and its shadow is 3:1 , then the angle of elevation of the sun is :

30{tex} ^{\circ} {/tex}

B

45{tex} ^{\circ} {/tex}

C

60{tex} ^{\circ} {/tex}

D

90{tex} ^{\circ} {/tex}

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Q 15. If two towers of height x and y subtend angles of 30{tex} ^{\circ} {/tex} and 60{tex} ^{\circ} {/tex} respectivelyat the centre of a line joining their feet, then x : y equals to

A

3 : 1

1 : 3

C

3:1

D

1:3

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Q 16. A wall 8 m long casts a shadow 5 m long. At same time, a tower casts a shadow 50 m long, then the height of tower is :

A

40 m

B

60 m

80 m

D

100 m

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Q 17. From the figure, the angle of depression of point C from the point P is :

A

90{tex} ^{\circ} {/tex}

B

60{tex} ^{\circ} {/tex}

30{tex} ^{\circ} {/tex}

D

45{tex} ^{\circ} {/tex}

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Q 18. A kite is flying at a height of 30 m from the ground. The length of string from the kite to the ground is 60 m.Assuming that there is no slack in the string, the angle of elevation of the kite at the ground is :

A

45{tex} ^{\circ} {/tex}

30{tex} ^{\circ} {/tex}

C

60{tex} ^{\circ} {/tex}

D

90{tex} ^{\circ} {/tex}

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Q 19. A 25 m ladder is placed against a vertical wall of a building. The foot of the ladder is 7m from the base of the building. If the top of the ladder slips 4m, then the foot of the ladder will slide

A

5

8m

C

9 m

D

15 m

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Q 20. The angle of elevation of the top of a tower as observed from a point on the ground is 'a' and on moving 'a' metres towards the tower, the angle of elevation is '{tex} \beta {/tex}'. Thus the height of the tower is :

A

{tex}a\frac{\left(\tan \alpha + \tan \beta\right)}{(\tan \beta - \tan \alpha)}{/tex}

{tex}a\frac{\left(\tan \alpha \tan \beta\right)}{(\tan \beta - \tan \alpha)}{/tex}

C

{tex}a\frac{\left(\tan \alpha \tan \beta\right)}{(\tan \beta + \tan \alpha)}{/tex}

D

{tex}a\frac{\left(\tan \alpha - \tan \beta\right)}{(\tan \beta + \tan \alpha)}{/tex}

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Q 21. A ladder is inclined to a wall making an angle of 30{tex} ^{\circ} {/tex} with it. A man is ascending the ladder at the rate of 2 metres/second. How fast is the approaching the wall ?

A

2 m/s

B

1.5 m/s

1 m/s

D

2.5 m/s

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Q 22. A round substance of radius r subtends an angle 2{tex} \alpha {/tex} at the eye of the observer while the angle of elevation of its centre is {tex} \beta {/tex}. Then the height of the centre of the balloon vertically above the horizontal level of eye is:

A

r {tex} \sin \beta \sin \alpha {/tex}

B

r {tex} \frac{\sin \alpha}{\sin \beta} {/tex}

C

r {tex} \frac{\sin \beta}{\sin \alpha} {/tex}

r {tex} \cosec\frac { \alpha}{2} {/tex} {tex} \sin \beta {/tex}

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Q 23. A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30{tex} ^{\circ} {/tex}.A girl standing on the roof of 20 m high building finds the angle of elevation of the same bird to be 45{tex} ^{\circ} {/tex}.
Both the boy and the girl are on opposite side of the bird. Then the distance of the bird from the girl is :

A

{tex} 30 \sqrt{3}{/tex} m

{tex} 30 \sqrt{2}{/tex} m

C

{tex} 20 \sqrt{2}{/tex} m

D

{tex} 20 \sqrt{3}{/tex} m

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Q 24. The angle of elevation of the top of a tower standing on a horizontal plane from a point A is {tex} \alpha {/tex}.After walking a distance 'd' towards the foot of the tower the angle of elevation is found to be {tex} \beta {/tex}. The height of tower is :

A

{tex}\frac{d}{\tan \beta - \tan \alpha}{/tex}

{tex}\frac{d}{\cot \alpha - \cot \beta}{/tex}

C

{tex}\frac{d}{\cot \alpha + \cot \beta}{/tex}

D

{tex}\frac{d}{\tan \beta + \tan \alpha}{/tex}

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Q 25. Two persons are 'a' metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevation of their tops to be complementary, then the height of the shorter person in metre is _________________.

A

{tex}\frac{a}{4}{/tex}

B

{tex}\frac{a}{\sqrt{2}}{/tex}

C

{tex}a \sqrt{2}{/tex}

{tex}\frac{a}{2\sqrt{2}}{/tex}