Class 10 Maths · Chapter 9

Some Applications of Trigonometry

43 Class 10 Maths questions on Some Applications of Trigonometry from the NCERT textbook, NCERT Exemplar and CBSE board papers 2026, each with its answer and a step-by-step solution.

CBSE Class 10 Maths previous year papers, with answers →

Questions · page 2 of 3

1. Q21 Exemplar · Exercise 8.3
   Find the ​angle of elevation of the ​sun ​when the ​shadow of ​a pole $h$ metres high is $\sqrt{3}h$ metres long.
   Show answer

   The angle of elevation of the sun is $30^{\circ }$.

   Step-by-step solution →
2. Q22 Exemplar · Exercise 8.3
   A ladder 15 metres ​long ​just ​reaches the top ​of ​a vertical wall. If the ​ladder makes an angle of $60^{\circ }$ with ​the wall, find the height of the wall.
   Show answer

   The height of the wall is $15\times \cos 60^{\circ }=7.5$ m.

   Step-by-step solution →
3. Q23 Exemplar · Exercise 8.3
   An observer $1.5$ metres tall is $20.5$ metres away from a ​tower $22$ ​metres high. Determine the angle of elevation ​of ​the ​top of ​the tower from the eye of the ​observer.
   Show answer

   The angle of elevation is $45^{\circ }$.

   Step-by-step solution →
4. Q24 CBSE 2026
   If the ​length ​of the shadow of a tower is $\sqrt{3}$ times that ​of ​its height, then altitude ​of the Sun is ​:

   1. (a)$45^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$15^{\circ }$
   Show answer

   (b) $30^{\circ }$

   Step-by-step solution →
5. Q25 CBSE 2026
   A car ​is moving away from the base ​of a $30$ m high tower. The angle ​of elevation of the ​top ​of the tower from the car at an ​instant, when the car is $10\sqrt{3}$ m away from the ​base of the tower, is :

   1. (a)$30^{\circ }$
   2. (b)$45^{\circ }$
   3. (c)$90^{\circ }$
   4. (d)$60^{\circ }$
   Show answer

   (d) $60^{\circ }$

   Step-by-step solution →
6. Q26 CBSE 2026
   From ​a point on ​the ​ground, ​which is $60$ m away ​from the foot of a vertical tower, ​the angle of elevation of the top ​of the ​tower is found to be $45^{\circ }$. The height (in metres) of the tower is :

   1. (a)$10\sqrt{3}$
   2. (b)$30\sqrt{3}$
   3. (c)$60$
   4. (d)$30$
   Show answer

   (c) $60$

   Step-by-step solution →
7. Q27 CBSE 2026
   At an ​instant, the length of ​shadow of a stick ​is found to be $\sqrt{3}$ times the length of the ​stick as shown in the ​figure below. ​The Sun's ​altitude at ​that instant is :

   1. (a)$30^{\circ }$
   2. (b)$45^{\circ }$
   3. (c)$60^{\circ }$
   4. (d)$90^{\circ }$
   Show answer

   (a) $30^{\circ }$

   Step-by-step solution →
8. Q28 CBSE 2026
   In the ​given figure, the angle of depression ​of ​the foot ​of building $CD$ from ​the top of ​tower $AB$ is :

   1. (a)$60^{\circ }$
   2. (b)$30^{\circ }$
   3. (c)$45^{\circ }$
   4. (d)$90^{\circ }$
   Show answer

   (a) $60^{\circ }$

   Step-by-step solution →
9. Q29 CBSE 2026
   In the adjoining figure, ​the angle ​of elevation ​of ​the point $C$ from the ​point $B$, ​is ​:

   1. (a)$30^{\circ }$
   2. (b)$45^{\circ }$
   3. (c)$22.5^{\circ }$
   4. (d)$67.5^{\circ }$
   Show answer

   (c) $22.5^{\circ }$

   Step-by-step solution →
10. Q30 CBSE 2026
    A wire is ​attached from ​a point $A$ on the ground to the top of a pole $BC$, ​making an ​angle of ​elevation as $60^{\circ }$. ​If $AB=5\sqrt{3}$ ​m, then length of the wire ​is

    1. (a)$10$ m
    2. (b)$10\sqrt{3}$ m
    3. (c)$15$ m
    4. (d)$\frac{5}{2}\sqrt{3}$ m
    Show answer

    (b) $10\sqrt{3}$ m

    Step-by-step solution →
11. Q31 CBSE 2026
    Two poles of equal heights ​are standing opposite each other on either side of the road, which is $80$ 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 and the distance of the point from the poles.
    Show answer

    Height of each pole $=20\sqrt{3}\approx 34.64$ m; the point is $20$ m from one pole and $60$ m from the other.

    Step-by-step solution →
12. Q32 CBSE 2026
    A kite is flying at a height of $60$ m above the ground level. Ravi, standing at the roof of the ​house is holding the string straight and observes the ​angle of elevation of kite ​as $30^{\circ }$. From the ​bottom of the same building, the angle of elevation of kite is $45^{\circ }$. Find the length of ​the ​string and ​height of roof from the ground. (Use $\sqrt{3}=1.73$)
    Show answer

    The length of the string is $40\sqrt{3}\approx 69.2$ m and the height of the roof from the ground is $60-20\sqrt{3}\approx 25.4$ m.

    Step-by-step solution →
13. Q33 CBSE 2026
    Two ​poles ​of equal heights are standing opposite to 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 $30^{\circ }$ and $60^{\circ }$ respectively. Find the height of ​the poles and the distances of the point from ​the poles. [Use $\sqrt{3}=1.732$]
    Show answer

    The height of each pole is $22.5\sqrt{3}\approx 38.97$ m. The point is $22.5$ m from the pole whose top is seen at $60^{\circ }$ and $67.5$ m from the pole whose top is seen at $30^{\circ }$.

    Step-by-step solution →
14. Q34 CBSE 2026
    The angle of elevation ​of the top of a building from the foot ​of ​the tower is $30^{\circ }$ and ​the angle of elevation of ​the top of the tower from the foot of ​the building is $60^{\circ }$. If the tower is $60$ m ​high, find the height ​of the building and the distance between the building and the tower. (Use $\sqrt{3}=1.73$)
    Show answer

    Height of the building $=20$ m; distance between the building and the tower $=20\sqrt{3}\approx 34.6$ m.

    Step-by-step solution →
15. Q35 CBSE 2026
    The angle of elevation ​of the top of a tower as observed from a point in a horizontal plane through the ​foot ​of the tower is $30^{\circ }$. ​When the observer moves towards the ​tower a distance ​of $100$ m, he finds the angle of elevation of the top to be $60^{\circ }$. Find the height of the tower and the ​distance of first position ​from the tower.
    Show answer

    Height of the tower $=50\sqrt{3}$ m $\approx 86.6$ m, and the distance of the first position from the tower $=150$ m.

    Step-by-step solution →
16. Q36 CBSE 2026
    Two pillars ​of equal heights stand ​on either side ​of ​a roadway $150$ m wide. From a point on the roadway between the pillars, ​the angles of elevation of the ​top of the pillars ​are $60^{\circ }$ and $30^{\circ }$ respectively. Find the height of the pillars ​and the position of the point from the pillars.
    Show answer

    Height of each pillar $=37.5\sqrt{3}\approx 64.95$ m. The point is $37.5$ m from the pillar subtending $60^{\circ }$ and $112.5$ m from the pillar subtending $30^{\circ }$.

    Step-by-step solution →
17. Q37 CBSE 2026
    A boy standing on a horizontal plane is flying a kite with a string of ​length $60$ m, at an angle of elevation of $30^{\circ }$. Another boy standing on ​the ​roof of a $20$ m high building, finds the angle ​of elevation of same kite to be $45^{\circ }$. If both the boys are on opposite sides of the kite, ​find the distance of the first boy ​from ​the base of the building. Also, find the ​height of the kite from the ground. (Use $\sqrt{3}=1.73$)
    Show answer

    The distance of the first boy from the base of the building is $30\sqrt{3}+10=61.9$ m, and the height of the kite from the ground is $30$ m.

    Step-by-step solution →
18. Q38 CBSE 2026
    Radio towers are used for transmitting ​a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station ​tower was built in two sections 'A' and ​'B'. Tower ​is ​supported by wires from a point 'O' (as shown in figure). Distance between the base of the tower and point 'O' is $6$ m. From point 'O', the angle of elevation of the top of the section 'B' is $30^{\circ }$ and the angle of elevation of ​the top of section 'A' is $60^{\circ }$. Based on ​the above ​information, answer the following questions :

    1. (i)Find the length of the wire from the point 'O' to the top of section 'B'.[1]
    2. (ii)Find the length of the wire from the point 'O' to the top of section 'A'.[1]
    3. (iii)(a)Find the distance $AB$.[2]
    4. (iii)(b)(OR) Find the area of $△OPB$.[2]
    Show answer

    (i) The length of the wire from O to the top of section B is $OB=4\sqrt{3}$ m (about $6.93$ m); (ii) The length of the wire from O to the top of section A is $OA=12$ m; (iii)(a) The distance $AB=4\sqrt{3}$ m (about $6.93$ m); (iii)(b) The area of $△OPB$ is $6\sqrt{3}$ m² (about $10.39$ m²).

    Step-by-step solution →
19. Q39 CBSE 2026
    Tejas ​is standing at ​the ​top of a building and observes a car at an angle of ​depression of $30^{\circ }$ as it approaches the base of the building at a uniform speed. $6$ seconds later, ​the ​angle of ​depression increases to $60^{\circ }$, and at that moment, the car is $25$ m away from the building. Based on the information given above, answer the following questions :

    1. (i)What is the height of the building ?[1]
    2. (ii)What is the distance between the two positions of the car ?[1]
    3. (iii)(a)What would be the total time taken by the car to reach the foot of the building from the starting point ?[2]
    4. (iii)(b)OR — What is the distance of the observer from the car when it makes an angle of $60^{\circ }$ ?[2]
    Show answer

    (i) The height of the building is $25\sqrt{3}$ m $\approx 43.3$ m; (ii) The distance between the two positions of the car is $50$ m; (iii)(a) The total time taken by the car to reach the foot of the building is $9$ seconds; (iii)(b) OR — The distance of the observer from the car at the $60^{\circ }$ position is $50$ m.

    Step-by-step solution →
20. Q40 CBSE 2026
    Climate change and global warming ​are influencing storm behaviour, particularly in terms ​of intensity and rainfall. Strong winds and storms often cause uprooting and/or breaking of trees, which damage the vehicles standing underneath the trees. On a particular day, during a high intensity storm, a tree broke such that its broken part formed ​an angle of $30^{\circ }$ with the ground. The distance between the base of the tree to the point where the top ​touches the ground ​is found to be $10$ m. Based ​on ​the above information, answer the following questions :

    1. (i)Represent the given information with the help of a neat and well labelled diagram.[1]
    2. (ii)Find the height above the ground at which the tree is broken.[1]
    3. (iii)(a)Find the height of the tree before it broke. (Use $\sqrt{3}=1.732$)[2]
    4. (iii)(b)OR : If another tree broke from the same height as in part (ii), but the broken part made a $60^{\circ }$ angle with the ground, find the total height of the tree.[2]
    Show answer

    (i) The situation is the right triangle $ABC$ shown in the diagram — stump $BC$ vertical, broken part $CA$ making $30^{\circ }$ with the ground, $AB=10$ m and the right angle at $B$; (ii) The tree is broken at a height of $\frac{10\sqrt{3}}{3}\approx 5.77$ m above the ground; (iii)(a) The height of the tree before it broke was $10\sqrt{3}=17.32$ m; (iii)(b) The total height of the second tree is $\frac{10\sqrt{3}+20}{3}\approx 12.44$ m.

    Step-by-step solution →