Download App

HEIGHTS AND DISTANCES [NEW] Maths - HEIGHTS AND DISTANCES [NEW]

CBSE - STD 10 - Maths (CBSE - English Medium). 68 questions in this chapter.

Question types

HEIGHTS AND DISTANCES [NEW] question types

68 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

68
Questions
5
Question groups
5
Question types
Sample Questions

HEIGHTS AND DISTANCES [NEW] questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
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
  • A
    $30^{\circ}$
  • B
    $45^{\circ}$
  • C
    $90^{\circ}$
  • ✓
    $60^{\circ}$

Answer: D.

View full solution →
Q 2M.C.Q (1 Marks)1 Mark
If the angle of elevation of a tower from a distance of 100 metres from its foot is $60^{\circ}$, then the height of the tower is
  • ✓
    $100 \sqrt{3} m$
  • B
    $\frac{100}{\sqrt{3}} m$
  • C
    $50 \sqrt{3} m$
  • D
    $\frac{200}{\sqrt{3}} m$

Answer: A.

View full solution →
Q 3M.C.Q (1 Marks)1 Mark
At some time of the dayy, if the leng th of the shadow of a vertical pole is equal to its height, the angle of eleation of Sun's altitude is
Image
  • ✓
    $45^{\circ}$
  • B
    $60^{\circ}$
  • C
    $30^{\circ}$
  • D
    $75^{\circ}$

Answer: A.

View full solution →
Q 4M.C.Q (1 Marks)1 Mark
If a pole 6 m high casts a shadow $2 \sqrt{3} m$ long on the ground, then sun's elevation is
  • A
    $60^{\circ}$
  • B
    $45^{\circ}$
  • ✓
    $30^{\circ}$
  • D
    $90^{\circ}$

Answer: C.

View full solution →
Q 5M.C.Q (1 Marks)1 Mark
A ladder makes an angle of $60^{\circ}$ with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length of the ladder (in metres) is
  • A
    $\frac{4}{\sqrt{3}}$
  • B
    $4 \sqrt{3}$
  • C
    $2 \sqrt{2}$
  • ✓
    4

Answer: D.

View full solution →
Q 6Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 ( $\Lambda$ ): If the shadow of a verlical pole is $\frac{1}{\sqrt{3}}$ of its height, then the altitude of the sum is $60^{\circ}$
Slatement-2 (R): If the sun's altitude is $45^{\circ}$, then the shadow of a vertical pole is same as its
Image
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement- 1 is True, Statement- 2 is False.
  • D
    Statement-1 is False, Statement- 2 is True.

Answer: B.

View full solution →
Q 7Assertion (A) & Reason (B) MCQ1 Mark
Statement-1 (A): If the angles of elevation of the top of a tower from the points at distances of 9 m and 16 m from the base of $a$ tower in the same line are complementary, then the height of the tower is 12 m .
Statement-2 (R): If the angle of elevation of a tower from two points at distances of $a$ and $b$ from its foot and in the same straight line with it are complementary, then the height of the tower is $\sqrt{a b}$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement- 1 is True, Statement- 2 is False.
  • D
    Statement-1 is False, Statement- 2 is True.

Answer: A.

View full solution →
Q 131 Marks Question1 Mark
Find the length of the shadow on the ground of a pole of height 18 m when angle of elevation $\theta$ of the sun is such that $\tan \theta=\frac{6}{7}$.
View full solution →
Q 151 Marks Question1 Mark
The ratio of the length of a vertical rod and the length of its shadow is $1: \sqrt{3}$. What is the angle of elevation of the sun at that moment?
View full solution →
Q 161 Marks Question1 Mark
An observer, 1.5 m tall, is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer.
View full solution →
Q 18Case study (4 Marks)4 Marks
One evening, Kaushik was in a park: Children wre playing cricket Birds were singing on a neurby trec of height 80 m . He obseried a bird on the trec at an angle of clevaton of $45^{\circ}$. When a sixcer was hin, a ball flew through the three frightening the bird to fly away. In 2 seconds, he observed the bird flying at the same height at an angle of clevations of $30^{\circ}$ and the ball flying touards him at the same height at an angle of elevation of $60^{\circ}$.
Image
(i) At what distance from the foot of the tree was he observing the bird sitting on the tree?
(ii) How far did the bird fly in the mentoned time?
(iii) After hitting the tree, how far did the ball travel in the sky when Kaushik saw the ball?
(iv) What is the specd of the bird in $m / min$ of it had flown $20(\sqrt{3}+1) m$ ?
View full solution →
Q 19Case study (4 Marks)4 Marks
A short circuit can happen on electric poles duc to several reasons, like:
(a) If the insulation is damaged or old, it may allow the hot wires to touch with neutral. This will cause a short circuit.
(b) If there are any loose wire connections or attachments, it will allow the live and neutral wires to touch. An electrician has to repair an clectric fault on a pole of height 5 m . He needs to reach a point 1 m below the top of the pole to undertake the repair work.
Based on the above information, answer the following questions:
Image
(i) What should be the length of the ladder that he should use which, when inclined at an angle of $60^{\circ}$ to the horizontal, cnables him to reach the required position?
(ii) How far from the foot of the pole should he place the foot of the ladder?
(iii) What is the length of the ladder if the foot is kept at a distance of 4 m from the foot of the pole?
View full solution →
Q 20Case study (4 Marks)4 Marks
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 buy wires from a point $O$.
Distance between the base of the tower and point O is 36 cm . 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 $45^{\circ}$.
(i) Find the length of the wire from the point $O$ to the top of Section B.
(ii) Find the distance $A B$.
(iii) Find the area of $\triangle O P B$.
(iv) Find the height of the Section A from the base of the tower.
Image
View full solution →
Q 21Case study (4 Marks)4 Marks
The following TV Tower was built in 1988 and is located in Pitampura, Delhi. It has an observation deck. Observe the picture given below:
Image
The TV Tower stands vertically on the ground. From a point ' $A$ ' on the ground, the angle of elevation of top of the tower (point ' $B$ ') is $60^{\circ}$. There is a point ' $C ^{\prime}$ ' on the tower which is 78 m (approx.) above the ground. The angle of elevation of the point $C$ from point $A$ is found to be $30^{\circ}$.
(i) Draw a well-labelled figure, based on the information given above.
(ii) Find the height of the tower and the distance of the tower from point $A$.
View full solution →
Q 22Case study (4 Marks)4 Marks
A helicopter lifts up 1000 feet over an island and spots a swimmer that need to be rescued. Using a distant land mark, the helicopter pilot determines the angle of depression.
Image
(i) As the angle of depression increases what will be the effect?
(a) The helicopter gets further from the island.
(b) The helicopter gets closer to the island.
(c) The swimmer gets closer to the island.
(d) The swimmer gets further from the island.
(ii) How does the swimmer's distance from island changes as the angle of depression is halved from $60^{\circ}$ to $30^{\circ}$ ?
(a) The swimmer's distance decreases to less than a quarter of his starting distance.
(b) The swimmer's distance from the island doubles
(c) The swimmer's distance from the island increases three times.
(d) The swimmer's distance from the island is halved.
(iii) For which angle of depression both the helicopter and swimmer's will be at same distance?
(a) $30^{\circ}$ $\qquad$ (b) $45^{\circ}$ $\qquad$ (c) $60^{\circ}$ $\qquad$ (d) $90^{\circ}$
(iv) Let the swimmer start out 1019 ft . from the island. If he swims half of the distance, what is angle of depression?)
(a) nearly $30^{\circ}$ $\qquad$ (b) nearly $45^{\circ}$ $\qquad$ (c) nearly $60^{\circ}$ $\qquad$ (d) nearly $90^{\circ}$
View full solution →
Browse all question groups ↑

Generate a HEIGHTS AND DISTANCES [NEW] paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App
Generate Paper FreeAll Maths chapters