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. 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.
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.
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?
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.
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.
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?
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.
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?
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.
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?
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.
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?
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?
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?
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?
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?
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?
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.
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?
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?
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.
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.
