Are these practice questions for Some Applications Of Trigonometry based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Some Applications Of Trigonometry free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Some Applications Of Trigonometry mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Some Applications Of Trigonometry for full coverage.

How many practice questions are there for Some Applications Of Trigonometry?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Some Applications Of Trigonometry Class 10 Mathematics Practice Questions with Answers

easy

Explain what is meant by the "angle of elevation".

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easy

The angle of elevation of the sun is

45^\circ

. Calculate the length of the shadow cast by a tower that is 100 m high.

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easy

Explain the primary difference between the angle of elevation and the angle of depression based on the observer's line of sight.

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easy

A student claims that to find the height of a tower, one only needs to know the length of its shadow. Critique this claim. What crucial piece of information is missing to formulate a solution?

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easy

Define the "angle of depression".

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easy

A ladder leaning against a vertical wall makes an angle of

60^\circ

with the ground. If the foot of the ladder is 2.5 m away from the wall, calculate the length of the ladder.

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easy

Formulate a mathematical expression for the height (h) of a vertical pole if the angle of elevation of its top from a point 'd' meters away from its base is

\theta

. You do not need to solve for any specific values.

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easy

An observer 1.6 m tall is

20\sqrt{3}

m away from a tower. The angle of elevation from his eye to the top of the tower is

30^\circ

. Calculate the height of the tower.

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easy

A vertical pole stands on the ground. From a point on the ground, the angle of elevation of the top of the pole is

30^\circ

. If a right-angled triangle is drawn to model this, identify the hypotenuse, the side opposite the

30^\circ

angle, and the side adjacent to the

30^\circ

angle.

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easy

Define the term "line of sight" as it is used in the context of trigonometry and heights.

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medium

Two ships are sailing in the sea on the same side of a lighthouse. The angles of depression of the two ships as observed from the top of the 100 m high lighthouse are

60^\circ

and

45^\circ

. A student calculates the distance between the ships using

\tan(60^\circ - 45^\circ)

. Critique this method and formulate the correct approach to find the distance.

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medium

Summarize the key steps to follow when drawing a diagram for a problem involving heights and distances.

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medium

A tree 12 m high is broken by the wind in such a way that its top touches the ground and makes an angle of

30^\circ

with the ground. At what height from the bottom did the tree break? (Use

\sqrt{3} = 1.73

)

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medium

A student solved a problem as follows: 'From the top of a 50 m building, the angle of depression to a car is

30^\circ

. The distance of the car from the building is

50 \sin 30^\circ

.' Critique the student's choice of trigonometric ratio and formulate the correct solution.

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medium

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is

60^\circ

. When he moves 40 m away from the bank, he finds the angle of elevation to be

30^\circ

. Formulate equations to find the height of the tree and the width of the river.

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medium

The shadow of a vertical tower on level ground is 30 m long when the sun's angle of elevation is

30^\circ

. Calculate the length of the shadow when the sun's elevation is

60^\circ

.

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medium

From the top of a cliff 50 m high, the angle of depression of a boat is

30^\circ

. Calculate the horizontal distance of the boat from the foot of the cliff.

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medium

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are

30^\circ

and

45^\circ

, respectively. If the bridge is at a height of 9 m from the banks, calculate the width of the river.

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medium

Describe a practical scenario where the concept of an angle of depression would be used.

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medium

A kite is flying at a height of 75 m from the ground level, attached to a string inclined at

60^\circ

to the horizontal. Calculate the length of the string, assuming there is no slack.

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medium

List the three essential measurements needed to determine the height of a tower if an observer of a known height is standing at some distance from it.

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medium

From the top of a cliff, the angle of depression to a boat is

\alpha

. After the boat travels 'd' meters directly towards the cliff, the angle of depression becomes

\beta

. Formulate a system of two equations involving the height of the cliff 'h' and its initial distance from the boat 'x'.

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medium

From the top of a building 15 m high, the angle of elevation of the top of a tower is

30^\circ

. From the bottom of the same building, the angle of elevation of the top of the tower is

60^\circ

. Calculate the height of the tower and the distance between the tower and the building.

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medium

Explain which trigonometric ratio (sine, cosine, or tangent) is most direct for finding the height of a pole when you know the length of its shadow and the sun's angle of elevation. Describe the relationship between these three quantities.

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medium

Justify the statement: 'The angle of elevation from point A on the ground to point B at the top of a tower is equal to the angle of depression from point B to point A.' Propose a diagram to support your reasoning.

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medium

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 7 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is

30^\circ

and that of the top of the flagstaff is

45^\circ

. Justify the steps to find the height of the tower.

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medium

Design a practical experiment to estimate the height of your school building. Propose the tools you would need, the procedure to follow, and formulate the mathematical model you would use to calculate the height. Evaluate potential sources of error in your experiment.

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medium

With the help of two separate, clearly labeled diagrams, explain the formation of (a) an angle of elevation and (b) an angle of depression.

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medium

Two towers, A and B, are observed from a point on the ground exactly midway between them. The angle of elevation to the top of tower A is

30^\circ

and to the top of tower B is

60^\circ

. Evaluate which tower is taller and justify your answer without calculation.

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medium

Describe a simple, real-life situation where you would need to understand the concept of an angle of elevation.

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medium

A vertical pole 6 m high casts a shadow

2\sqrt{3}

m long on the ground. Examine the Sun's angle of elevation at that moment.

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medium

A man on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a cliff as

60^\circ

and the angle of depression of the base of the cliff as

30^\circ

. Calculate the distance of the cliff from the ship and the height of the cliff.

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medium

In a right-angled triangle ABC, right-angled at B, an observer is at point C looking at the top of a vertical pole AB. Name the angle of elevation in this scenario.

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hard

Derive a general formula for the height 'h' of a tower when the angles of elevation of its top from two points at distances 'a' and 'b' from its foot, on the same straight line, are complementary. Justify each step of your derivation.

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hard

Explain why the angle of depression from an observation point A to an object B is always equal to the angle of elevation from the object B to the observation point A.

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hard

Propose a method using trigonometry to determine the width of a river without crossing it. List the measurements you would need to take.

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hard

The angle of elevation of a cloud from a point 'h' meters above a lake is

\alpha

and the angle of depression of its reflection in the lake is

\beta

. Create a proof to show that the height of the cloud from the surface of the lake is

H = h \left( \frac{\tan \beta + \tan \alpha}{\tan \beta - \tan \alpha} \right)

.

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hard

Design a word problem where the solution requires using both the sine and cosine ratios to find the final answer. The problem must involve an object, such as a ladder against a wall. Formulate the steps to solve your created problem.

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hard

The angle of elevation of a cloud from a point 60 m above a lake is

30^\circ

and the angle of depression of the reflection of the cloud in the lake is

60^\circ

. Analyze the situation to find the height of the cloud from the surface of the lake.

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hard

You need to find the height of a tall tree on level ground. List the practical steps and measurements you would take. Explain how these measurements correspond to the elements of a right-angled triangle.

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hard

An airplane is flying at a constant height. An observer on the ground sees the plane at an angle of elevation of

60^\circ

. After 10 seconds, the angle of elevation from the same point becomes

30^\circ

. If the plane is flying at a speed of

360

km/hr, create a model to determine the constant height at which the plane is flying.

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hard

Explain, with the help of a labeled diagram, the trigonometric method to determine the width of a river if you can only take measurements from one bank.

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hard

The angles of elevation of the top of a tower from two points at distances of 5 m and 20 m from the base of the tower and in the same straight line with it are complementary. Analyze the given information to find the height of the tower.

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hard

An aeroplane flying horizontally 1 km above the ground is observed at an angle of elevation of

60^\circ

. After 10 seconds, its elevation from the same point of observation is

30^\circ

. Find the speed of the aeroplane in km/hr. (Use

\sqrt{3} = 1.732

)

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Some Applications Of TrigonometryClass 10 Mathematics Practice Questions