Q. From a point A, the angle of elevation of the top of a building is 45 degrees. If the height of the building is 20 meters, how far is point A from the base of the building?
A.
10 m
B.
20 m
C.
30 m
D.
40 m
Solution
Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
A.
50 m
B.
60 m
C.
70 m
D.
80 m
Solution
Using tan(30°) = height/100, we have 1/√3 = height/100. Therefore, height = 100/√3 ≈ 57.74 m.
Q. From a point on the ground, the angle of elevation of the top of a hill is 30 degrees. If the height of the hill is 50 meters, how far is the point from the base of the hill?
A.
50 m
B.
75 m
C.
100 m
D.
125 m
Solution
Using tan(30°) = height/distance, we have 1/√3 = 50/distance. Therefore, distance = 50√3 ≈ 86.6 m.
Q. From a point on the ground, the angle of elevation to the top of a 40 m high building is 45 degrees. How far is the point from the base of the building?
A.
40 m
B.
20 m
C.
30 m
D.
50 m
Solution
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 40/1 = 40 m.
Q. From a point on the ground, the angle of elevation to the top of a building is 45 degrees. If the building is 50 meters tall, how far is the point from the base of the building?
Q. From a point on the ground, the angle of elevation to the top of a hill is 30 degrees. If the distance from the point to the base of the hill is 100 meters, what is the height of the hill?
A.
100√3 m
B.
50 m
C.
100 m
D.
50√3 m
Solution
Using tan(30°) = height/distance, we have height = distance * tan(30°) = 100 * (1/√3) = 100/√3 = 50 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 20 m, how far is the point from the base of the hill?
A.
20 m
B.
10 m
C.
30 m
D.
40 m
Solution
Using tan(45°) = height/distance, we have 1 = 20/distance. Therefore, distance = 20 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 50 m, how far is the point from the base of the hill?
A.
25 m
B.
50 m
C.
70 m
D.
100 m
Solution
Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 100 m, how far is the point from the base of the hill?
A.
100 m
B.
50 m
C.
200 m
D.
150 m
Solution
Using tan(45°) = height/distance, we have distance = height/tan(45°) = 100/1 = 100 m.
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 100 meters away from the base of the hill, what is the height of the hill?
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the height of the hill is 40 m, how far is the point from the base of the hill?
A.
20 m
B.
40 m
C.
60 m
D.
80 m
Solution
Using tan(45°) = height/distance, we have 1 = 40/distance. Therefore, distance = 40 m.
Q. From a point on the ground, the angle of elevation to the top of a tower is 60 degrees. If the tower is 30 m high, how far is the point from the base of the tower?
A.
15 m
B.
30 m
C.
20 m
D.
10 m
Solution
Using tan(60°) = height/distance, we have √3 = 30/distance. Therefore, distance = 30/√3 m.
Q. From the top of a 20-meter high building, the angle of depression to a car parked on the ground is 60 degrees. How far is the car from the base of the building?
Q. From the top of a 50 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?
A.
25 m
B.
50 m
C.
70 m
D.
100 m
Solution
Using tan(45°) = height/distance, we have 1 = 50/distance. Therefore, distance = 50 m.
Q. From the top of a 50-meter 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?
Q. From the top of a 60 m high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?
A.
60√3 m
B.
30√3 m
C.
60 m
D.
30 m
Solution
Using tan(30°) = height/distance, we have distance = height/tan(30°) = 60/√3 = 60√3 m.
Q. If a person is standing 50 meters away from a building and the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Trigonometry is a crucial 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. Practicing MCQs and objective questions is essential for effective exam preparation, as it helps you identify important questions and strengthens your understanding of key concepts.
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
Solving Triangles: Area and Perimeter Calculations
Exam Relevance
Trigonometry is a vital topic in the CBSE curriculum and is frequently tested in State Boards, NEET, and JEE exams. Students can expect questions that assess their understanding of trigonometric ratios, identities, and real-world applications. Common question patterns include solving equations, proving identities, and applying concepts to practical scenarios.
Common Mistakes Students Make
Confusing the values of trigonometric ratios in different quadrants.
Neglecting to apply the correct identities while simplifying expressions.
Misinterpreting the angle measures, especially in height and distance problems.
Overlooking the importance of unit circle concepts in graphing functions.
FAQs
Question: What are some important Trigonometry MCQ questions for exams? Answer: Important questions often include finding the values of trigonometric ratios, solving trigonometric equations, and applying identities to simplify expressions.
Question: How can I effectively prepare for Trigonometry objective questions? Answer: Regular practice of MCQs, understanding key concepts, and reviewing mistakes can significantly improve your preparation.
Now is the time to enhance your Trigonometry skills! Dive into our practice MCQs and test your understanding to excel in your exams.
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