Trigonometry Study Resources for Competitive Exams

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Trigonometry MCQ & Objective Questions

Trigonometry is a crucial branch of mathematics that plays a significant role in various school and competitive exams. Mastering this topic not only enhances your understanding of angles and their relationships but also boosts your confidence in tackling objective questions. Practicing MCQs and important questions in Trigonometry helps solidify concepts and improves your exam preparation, ensuring you score better in your assessments.

What You Will Practise Here

Fundamental Trigonometric Ratios: Sine, Cosine, and Tangent
Trigonometric Identities and Their Applications
Graphs of Trigonometric Functions
Inverse Trigonometric Functions
Applications of Trigonometry in Real-Life Problems
Solving Right-Angled Triangles
Height and Distance Problems

Exam Relevance

Trigonometry is a vital topic in various examinations, including CBSE, State Boards, NEET, and JEE. Questions often focus on fundamental concepts, problem-solving, and application-based scenarios. Common patterns include direct MCQs, numerical problems, and theoretical questions that assess your understanding of trigonometric principles and their applications.

Common Mistakes Students Make

Confusing the ratios of different angles, especially in right-angled triangles.
Misapplying trigonometric identities in problem-solving.
Neglecting to check the domain and range of inverse trigonometric functions.
Overlooking the importance of unit circle in understanding trigonometric functions.

FAQs

Question: What are the basic trigonometric ratios?
Answer: The basic trigonometric ratios are Sine, Cosine, and Tangent, which relate the angles of a triangle to the lengths of its sides.

Question: How can I improve my Trigonometry skills for exams?
Answer: Regular practice of Trigonometry MCQ questions and understanding the underlying concepts will significantly enhance your skills and exam readiness.

Now is the time to take charge of your Trigonometry preparation! Dive into our practice MCQs and important questions to test your understanding and excel in your exams.

Heights & Distances Trigonometric Ratios & Identities

Q. A 12-meter tall pole casts a shadow of 6 meters. What is the angle of elevation of the sun?

A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees

Solution

Using tan(θ) = height / shadow length, we have θ = tan⁻¹(12/6) = tan⁻¹(2) which corresponds to approximately 60 degrees.

Correct Answer: C — 60 degrees

Q. A flagpole is 12 meters high. If the angle of elevation from a point 16 meters away from the base of the flagpole is θ, what is tan(θ)?

A. 3/4
B. 4/3
C. 1/2
D. 2/1

Solution

tan(θ) = height / distance = 12 / 16 = 3/4.

Correct Answer: B — 4/3

Q. A flagpole is 12 meters tall. If the angle of elevation from a point 16 meters away from the base of the flagpole is θ, what is tan(θ)?

A. 0.75
B. 0.5
C. 0.8
D. 1

Solution

tan(θ) = height/distance = 12/16 = 0.75.

Correct Answer: A — 0.75

Q. A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?

A. 40 meters
B. 20√2 meters
C. 30 meters
D. 50 meters

Solution

Using tan(45°) = height / distance, we have distance = height / tan(45°) = 40 / 1 = 40 meters.

Correct Answer: B — 20√2 meters

Q. A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 30 degrees, how far is the point from the base of the kite?

A. 40√3 meters
B. 20√3 meters
C. 30 meters
D. 50 meters

Solution

Using the tangent function, tan(30) = 40 / distance. Therefore, distance = 40 / tan(30) = 40√3 meters.

Correct Answer: A — 40√3 meters

Q. A kite is flying at a height of 40 meters. If the angle of elevation from a point on the ground to the kite is 60 degrees, how far is the point from the base of the kite's height?

A. 20√3 meters
B. 40 meters
C. 30 meters
D. 10√3 meters

Solution

Using tan(60) = 40/distance, distance = 40/tan(60) = 40/√3 = 20√3 meters.

Correct Answer: A — 20√3 meters

Q. A kite is flying at a height of 50 meters. If the angle of elevation from a point on the ground to the kite is 45 degrees, how far is the point from the base of the kite?

A. 50 meters
B. 25 meters
C. 35 meters
D. 70 meters

Solution

Using the tangent function, tan(45) = 50 / distance. Therefore, distance = 50 / tan(45) = 50 meters.

Correct Answer: A — 50 meters

Q. A ladder 10 meters long leans against a wall, forming an angle of 60 degrees with the ground. How high does the ladder reach on the wall?

A. 5 meters
B. 8.66 meters
C. 10 meters
D. 7.5 meters

Solution

Using sin(60°) = height / ladder length, we have height = ladder length * sin(60°) = 10 * (√3/2) = 5√3 ≈ 8.66 meters.

Correct Answer: B — 8.66 meters

Q. A ladder 10 meters long leans against a wall, making an angle of 60 degrees with the ground. How high does the ladder reach on the wall?

A. 5 meters
B. 10 meters
C. 8.66 meters
D. 7.5 meters

Solution

Using sine, height = 10 * sin(60) = 10 * (√3/2) = 5√3 ≈ 8.66 meters.

Correct Answer: C — 8.66 meters

Q. A ladder leans against a wall making a 60-degree angle with the ground. If the foot of the ladder is 4 meters from the wall, how high does the ladder reach on the wall?

A. 2√3 meters
B. 4√3 meters
C. 4 meters
D. 2 meters

Solution

Using sine, height = 4 * tan(60) = 4 * √3 = 4√3 meters.

Correct Answer: B — 4√3 meters

Q. A person is 40 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

A. 20√3 meters
B. 30 meters
C. 40 meters
D. 10√3 meters

Solution

Using tan(30°) = height / distance, we have height = distance * tan(30°) = 40 * (1/√3) = 40/√3 = 20√3 meters.

Correct Answer: A — 20√3 meters

Q. A person is looking at the top of a 10-meter tall building from a distance of 20 meters. What is the angle of elevation?

A. 26.57 degrees
B. 30 degrees
C. 45 degrees
D. 60 degrees

Solution

Using the tangent function, tan(angle) = 10 / 20. Therefore, angle = arctan(0.5) = 26.57 degrees.

Correct Answer: A — 26.57 degrees

Q. A person is standing 20 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 30 degrees, what is the height of the flagpole?

A. 10√3 meters
B. 20 meters
C. 15 meters
D. 5√3 meters

Solution

Using the tangent function, tan(30) = height / 20. Therefore, height = 20 * tan(30) = 20 * (1/√3) = 10√3 meters.

Correct Answer: A — 10√3 meters

Q. A person is standing 25 meters away from a building and measures the angle of elevation to the top of the building as 36.87 degrees. What is the height of the building?

A. 15 meters
B. 20 meters
C. 10 meters
D. 25 meters

Solution

Let h be the height of the building. tan(36.87°) = h/25. Therefore, h = 25 * tan(36.87°) = 25 * 0.75 = 18.75 meters.

Correct Answer: A — 15 meters

Q. A person is standing 25 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees. What is the height of the building?

A. 25/√3 meters
B. 15 meters
C. 20 meters
D. 10 meters

Solution

Using tan(30) = height/25, height = 25 * (1/√3) = 25/√3 meters.

Correct Answer: A — 25/√3 meters

Q. A person is standing 25 meters away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

A. 25√3 meters
B. 15 meters
C. 20 meters
D. 30 meters

Solution

Using tan(60°) = height / distance, we have height = distance * tan(60°) = 25 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

Q. A person is standing 25 meters away from a building. If the angle of elevation to the top of the building is 36.87 degrees, what is the height of the building?

A. 15 meters
B. 20 meters
C. 25 meters
D. 30 meters

Solution

Using the tangent function, tan(36.87) = height / 25. Therefore, height = 25 * tan(36.87) = 25 * 0.75 = 18.75 meters.

Correct Answer: A — 15 meters

Q. A person is standing 25 meters away from a cliff and sees the top of the cliff at an angle of elevation of 60 degrees. What is the height of the cliff?

A. 25√3 meters
B. 30 meters
C. 20 meters
D. 15 meters

Solution

Using tan(60) = height/25, height = 25 * √3 = 25√3 meters.

Correct Answer: A — 25√3 meters

Q. A person is standing 25 meters away from a cliff and sees the top of the cliff at an angle of elevation of 75 degrees. What is the height of the cliff?

A. 25√3 meters
B. 25√2 meters
C. 25√5 meters
D. 25 meters

Solution

Using tan(75°) = height / 25, height = 25 * tan(75°) ≈ 25 * 3.732 = 93.3 meters.

Correct Answer: A — 25√3 meters

Q. A person is standing 30 meters away from a flagpole. If the angle of elevation to the top of the flagpole is 30 degrees, what is the height of the flagpole?

A. 15√3 meters
B. 10 meters
C. 5√3 meters
D. 20 meters

Solution

Using the tangent function, tan(30) = height / 30. Therefore, height = 30 * tan(30) = 30 * (1/√3) = 10√3 meters.

Correct Answer: A — 15√3 meters

Q. A person is standing 40 meters away from a building and sees the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

A. 40 meters
B. 30 meters
C. 20 meters
D. 50 meters

Solution

Using tan(45) = height/40, height = 40 * tan(45) = 40 meters.

Correct Answer: A — 40 meters

Q. A person is standing 40 meters away from a building and sees the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

A. 20√3 meters
B. 40 meters
C. 30 meters
D. 50 meters

Solution

Using tan(60°) = height / 40, height = 40 * tan(60°) = 40 * √3 ≈ 69.28 meters.

Correct Answer: A — 20√3 meters

Q. A person is standing 40 meters away from a statue and measures the angle of elevation to the top of the statue as 53.13 degrees. What is the height of the statue?

A. 30 meters
B. 20 meters
C. 25 meters
D. 15 meters

Solution

Let h be the height of the statue. tan(53.13°) = h/40. Therefore, h = 40 * tan(53.13°) = 40 * 1.6 = 64 meters.

Correct Answer: A — 30 meters

Q. A person is standing 40 meters away from a tower and sees the top of the tower at an angle of elevation of 60 degrees. What is the height of the tower?

A. 20√3 meters
B. 40 meters
C. 30 meters
D. 10√3 meters

Solution

Using tan(60) = height/40, height = 40 * √3 = 20√3 meters.

Correct Answer: A — 20√3 meters

Q. A person is standing 50 meters away from a cliff. If the angle of elevation to the top of the cliff is 60 degrees, what is the height of the cliff?

A. 25√3 meters
B. 50 meters
C. 30 meters
D. 40 meters

Solution

Using the tangent function, tan(60) = height / 50. Therefore, height = 50 * tan(60) = 50 * √3 = 50√3 meters.

Correct Answer: A — 25√3 meters

Q. A person standing 30 meters away from a building observes the angle of elevation to the top of the building as 60 degrees. What is the height of the building?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 25 meters

Solution

Using tan(60) = height/30, height = 30 * √3 = 15√3 meters.

Correct Answer: A — 15√3 meters

Q. A person standing 30 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 10√3 meters

Solution

Using tan(60°) = height / distance, we have height = distance * tan(60°) = 30 * √3 = 15√3 meters.

Correct Answer: A — 15√3 meters

Q. A person standing 30 meters away from a cliff measures the angle of elevation to the top of the cliff as 60 degrees. How tall is the cliff?

A. 15√3 meters
B. 30 meters
C. 20 meters
D. 10√3 meters

Solution

Let h be the height of the cliff. tan(60°) = h/30. Therefore, h = 30 * tan(60°) = 30 * √3 = 15√3 meters.

Correct Answer: A — 15√3 meters

Q. A tree casts a shadow of 15 meters when the angle of elevation of the sun is 30 degrees. What is the height of the tree?

A. 5√3 meters
B. 15 meters
C. 10 meters
D. 7.5 meters

Solution

Using the tangent function, tan(30) = height / 15. Therefore, height = 15 * tan(30) = 15 * (1/√3) = 5√3 meters.

Correct Answer: A — 5√3 meters

Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the point is 10 meters away from the building, what is the height of the building?

A. 10 meters
B. 5 meters
C. 15 meters
D. 20 meters

Solution

Using the tangent function, tan(45) = height / 10. Therefore, height = 10 * tan(45) = 10 meters.

Correct Answer: A — 10 meters

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