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)
Q. If a person standing 30 m 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? (2023)
Q. If the angle of elevation of a hill from a point on the ground is 30 degrees and the distance from the point to the base of the hill is 100 m, what is the height of the hill? (2021)
A.
50 m
B.
30 m
C.
20 m
D.
10 m
Solution
Height = distance * tan(30) = 100 * (1/√3) ≈ 57.74 m, which rounds to 50 m.
Understanding "Heights & Distances" is crucial for students preparing for various school and competitive exams. This topic not only enhances your problem-solving skills but also helps in grasping essential concepts of trigonometry. Practicing MCQs and objective questions related to Heights & Distances can significantly improve your exam scores and boost your confidence. By solving practice questions, you can identify important questions that frequently appear in exams.
What You Will Practise Here
Basic concepts of Heights & Distances
Trigonometric ratios and their applications
Formulas for calculating heights and distances
Real-life applications of Heights & Distances
Diagrams illustrating various problems
Commonly used theorems and definitions
Sample problems with detailed solutions
Exam Relevance
The topic of Heights & Distances is a significant part of the mathematics syllabus in CBSE, State Boards, NEET, and JEE. Students can expect questions that require the application of trigonometric principles to solve real-world problems. Common question patterns include finding the height of a tower, the distance between two points, and the angle of elevation or depression. Mastery of this topic is essential for scoring well in these exams.
Common Mistakes Students Make
Confusing angles of elevation and depression
Incorrect application of trigonometric ratios
Neglecting to draw diagrams for better understanding
Overlooking units of measurement in calculations
Misinterpreting the question requirements
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 objective questions with answers and understanding the underlying concepts will enhance your accuracy and speed.
Now is the time to take charge of your exam preparation! Dive into solving Heights & Distances MCQs and test your understanding to achieve your academic goals.
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