The topic of "Heights & Distances" is crucial for students preparing for various school and competitive exams in India. Understanding this concept not only enhances your mathematical skills but also boosts your confidence in tackling objective questions. Practicing MCQs related to Heights & Distances helps you identify important questions and solidifies your exam preparation, ensuring you score better in your assessments.
What You Will Practise Here
Understanding the basic concepts of Heights & Distances
Application of trigonometric ratios in real-life scenarios
Calculating heights and distances using angles of elevation and depression
Important formulas related to Heights & Distances
Solving practical problems and word problems
Interpreting diagrams and visual representations
Common applications in competitive exams
Exam Relevance
The topic of Heights & Distances is frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that require the application of trigonometric principles to calculate heights and distances in various contexts. Common question patterns include finding the height of a tower given the angle of elevation from a certain distance or determining the distance between two points using angles of depression.
Common Mistakes Students Make
Confusing angles of elevation with angles of depression
Misapplying trigonometric ratios in problem-solving
Overlooking the importance of diagram interpretation
Neglecting to check units of measurement
Rushing through calculations leading to simple arithmetic errors
FAQs
Question: What are the key formulas for Heights & Distances? Answer: The key formulas include h = d * tan(θ) for height and d = h / tan(θ) for distance, where h is height, d is distance, and θ is the angle of elevation or depression.
Question: How can I improve my accuracy in Heights & Distances MCQs? Answer: Regular practice of Heights & Distances MCQ questions, along with reviewing common mistakes, can significantly improve your accuracy and confidence.
Start solving practice MCQs today to test your understanding of Heights & Distances and enhance your exam readiness. Remember, consistent practice is the key to success!
Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the distance from the point to the base of the hill is 10 meters, 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 point is 10 meters away from the base of the hill, what is the height of the hill?
A.
10 meters
B.
5 meters
C.
15 meters
D.
20 meters
Solution
Let h be the height of the hill. tan(45°) = h/10. Therefore, h = 10 * tan(45°) = 10 * 1 = 10 meters.
Q. From a point on the ground, the angle of elevation to the top of a hill is 53.13 degrees. If the point is 40 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 tower is 30 degrees. If the tower is 20 meters tall, how far is the point from the base of the tower?
A.
20√3 meters
B.
10√3 meters
C.
30 meters
D.
40 meters
Solution
Using the tangent function, tan(30) = 20 / distance. Therefore, distance = 20 / tan(30) = 20√3 meters.
