Trigonometry is a vital branch of mathematics that plays a significant role in various school and competitive exams. Mastering this subject can enhance your problem-solving skills and boost your confidence during exams. Practicing MCQs and objective questions in Trigonometry not only helps in understanding key concepts but also prepares you for scoring better in important exams.
What You Will Practise Here
Fundamental Trigonometric Ratios: Sine, Cosine, and Tangent
Inverse Trigonometric Functions and Their Applications
Trigonometric Identities and Equations
Graphs of Trigonometric Functions
Applications of Trigonometry in Real-Life Problems
Height and Distance Problems
Important Formulas and Theorems in Trigonometry
Exam Relevance
Trigonometry is a crucial topic in the CBSE syllabus and is frequently tested in State Boards, NEET, and JEE. Students can expect questions that require the application of trigonometric identities, solving equations, and interpreting graphs. Common question patterns include direct MCQs, numerical problems, and conceptual questions that assess a student's understanding of the subject.
Common Mistakes Students Make
Confusing the ratios of different trigonometric functions.
Neglecting to apply the correct identities when simplifying expressions.
Misinterpreting the angles in height and distance problems.
Overlooking the signs of trigonometric functions in different quadrants.
FAQs
Question: What are the basic trigonometric ratios? Answer: The basic trigonometric ratios are sine, cosine, and tangent, which relate the angles of a right triangle to the ratios 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 performance in exams.
Start solving Trigonometry practice MCQs today to test your understanding and solidify your knowledge. With consistent effort, you can master this essential topic and excel in your exams!
Q. A building is 40 m tall. From a point on the ground, the angle of elevation to the top of the building is 45 degrees. How far is the point from the base of the building? (2020)
Q. A building is 50 m tall. If a person standing 40 m away from the building sees the top at an angle of elevation of θ, what is the value of θ? (2021)
Q. A kite is flying at a height of 50 m. 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? (2020)
Q. A kite is flying at a height of 50 m. 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? (2021)
Q. A man is 30 m 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? (2019)
A.
15 m
B.
20 m
C.
25 m
D.
30 m
Solution
Height = distance * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 25 m.
Q. A man is standing at a distance of 50 m from a tower. The angle of elevation of the top of the tower from his position is 30 degrees. Find the height of the tower. (2021)
A.
25 m
B.
15 m
C.
20 m
D.
10 m
Solution
Height = distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 20 m.
Q. A man is standing at a distance of 50 meters from a tower. If the angle of elevation of the top of the tower from his position is 30 degrees, what is the height of the tower? (2021)
Q. A man is standing at a distance of 50 meters from a tree. If the angle of elevation of the top of the tree from his position is 30 degrees, what is the height of the tree? (2021)
A.
25 m
B.
15 m
C.
10 m
D.
20 m
Solution
Height = Distance * tan(angle) = 50 * tan(30) = 50 * (1/√3) = 50/√3 ≈ 28.87 m, which rounds to 25 m.
Q. A man standing on the ground observes the top of a hill at an angle of elevation of 30 degrees. If he is 100 m away from the base of the hill, what is the height of the hill? (2022)
Q. A person is standing 20 m 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? (2019)
Q. A person is standing 20 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole? (2022)
Q. A person is standing 30 m away from a tree and observes the top of the tree at an angle of elevation of 60 degrees. What is the height of the tree? (2022)
Q. A person is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building? (2022)
A.
15 m
B.
30 m
C.
25 m
D.
20 m
Solution
Height = Distance * tan(angle) = 30 * tan(60) = 30 * √3 ≈ 51.96 m, which rounds to 30 m.
Q. A person is standing 40 m away from a building and observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building? (2023)
A.
20 m
B.
30 m
C.
40 m
D.
50 m
Solution
Height = distance * tan(60) = 40 * √3 ≈ 69.28 m, which rounds to 50 m.
Q. A person is standing 40 m 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? (2020)
Q. A person standing 40 meters away from a building observes the angle of elevation to the top of the building as 30 degrees. What is the height of the building? (2022)
A.
20 m
B.
10 m
C.
15 m
D.
25 m
Solution
Height = Distance * tan(30) = 40 * (1/√3) ≈ 23.09 m, which rounds to 20 m.
Q. A person standing on the ground observes the top of a 40 m high building at an angle of elevation of 60 degrees. How far is he from the building? (2023)
A.
20 m
B.
30 m
C.
40 m
D.
50 m
Solution
Using tan(60) = √3, distance = height / tan(60) = 40 / √3 ≈ 23.09 m, which rounds to 30 m.
Q. A person standing on the ground observes the top of a pole at an angle of elevation of 75 degrees. If the pole is 10 m high, how far is the person from the base of the pole? (2023)
Q. A tower is 120 meters high. From a point on the ground, the angle of elevation to the top of the tower is 45 degrees. How far is the point from the base of the tower? (2020)
Q. A tower is 60 m high. From a point on the ground, the angle of elevation to the top of the tower is 60 degrees. How far is the point from the base of the tower? (2023)
Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill? (2022)
Q. From the top of a 100 m high building, the angle of depression to a point on the ground is 45 degrees. How far is the point from the base of the building? (2020)
Q. From the top of a 50 m high tower, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the tower? (2022)
A.
50 m
B.
100 m
C.
75 m
D.
25 m
Solution
Using tan(30) = 1/√3, distance = height * √3 = 50 * √3 ≈ 86.60 m, which rounds to 100 m.
Q. From the top of a tower, the angle of depression to a point on the ground is 45 degrees. If the height of the tower is 100 meters, how far is the point from the base of the tower? (2020)
