Railways Exam > Railways Questions > The elevation angles of the top of a tower 9...
Start Learning for Free
The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)
- a)133m
- b)142m
- c)150m
- d)167m
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The elevation angles of the top of a tower 90 m high, from two points...
Let AB be the tower and C and D the two points.
Now AB/BC = tan45∘=1
AB = BC = 90
Also AB/BD = tan60∘ = √3
BD = 90/√3 = 30√3
Hence CD = CB + BD = 90 + 30√3 = 90 + 51.96 = 141.96 ≈ 142m
Most Upvoted Answer
The elevation angles of the top of a tower 90 m high, from two points...
To find the distance between the two points on the ground level, we can use trigonometry. Let's break down the problem step by step:
Given:
- Height of the tower = 90 m
- Elevation angle from one point = 45°
- Elevation angle from the other point = 60°
Finding the distance:
1. Draw a diagram to visualize the problem. Label the tower as "T", the two points on the ground as "A" and "B", and the height of the tower as 90 m.
2. We can see that we have a right-angled triangle formed by the tower and the line connecting the two points on the ground. Let's label the distance between the two points as "x".
3. Using trigonometry, we can relate the angles and sides of the triangle:
- For angle A: tan(A) = opposite/adjacent = 90/x
- For angle B: tan(B) = opposite/adjacent = 90/(x + d)
Where d is the distance between the two points on the ground.
4. Simplify the equations:
- tan(45°) = 90/x
- tan(60°) = 90/(x + d)
Using the value of √3 = 1.732:
- 1 = 90/x
- √3 = 90/(x + d)
5. Solve the equations:
- From the first equation, x = 90.
- Substitute the value of x in the second equation:
√3 = 90/(90 + d)
√3 = 1/(1 + d/90)
√3(1 + d/90) = 1
√3 + d/90 = 1
d/90 = 1 - √3
d = 90(1 - √3)
6. Calculate the value of d using a calculator:
d ≈ 142
Therefore, the distance between the two points on the ground level is approximately 142 meters. Hence, the correct answer is option B.
Given:
- Height of the tower = 90 m
- Elevation angle from one point = 45°
- Elevation angle from the other point = 60°
Finding the distance:
1. Draw a diagram to visualize the problem. Label the tower as "T", the two points on the ground as "A" and "B", and the height of the tower as 90 m.
2. We can see that we have a right-angled triangle formed by the tower and the line connecting the two points on the ground. Let's label the distance between the two points as "x".
3. Using trigonometry, we can relate the angles and sides of the triangle:
- For angle A: tan(A) = opposite/adjacent = 90/x
- For angle B: tan(B) = opposite/adjacent = 90/(x + d)
Where d is the distance between the two points on the ground.
4. Simplify the equations:
- tan(45°) = 90/x
- tan(60°) = 90/(x + d)
Using the value of √3 = 1.732:
- 1 = 90/x
- √3 = 90/(x + d)
5. Solve the equations:
- From the first equation, x = 90.
- Substitute the value of x in the second equation:
√3 = 90/(90 + d)
√3 = 1/(1 + d/90)
√3(1 + d/90) = 1
√3 + d/90 = 1
d/90 = 1 - √3
d = 90(1 - √3)
6. Calculate the value of d using a calculator:
d ≈ 142
Therefore, the distance between the two points on the ground level is approximately 142 meters. Hence, the correct answer is option B.
Attention Railways Students!
To make sure you are not studying endlessly, EduRev has designed Railways study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Railways.
|
Explore Courses for Railways exam
|
|
Top Courses for RailwaysView all
The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer?
Question Description
The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer?.
The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Railways.
Download more important topics, notes, lectures and mock test series for Railways Exam by signing up for free.
Here you can find the meaning of The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The elevation angles of the top of a tower 90 m high, from two points on the ground level on its opposite sides are 45° and 60°. What is the distance between the two points (rounded off to the nearest integer)? (√3 = 1.732)a)133mb)142mc)150md)167mCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Railways tests.
|
|
Explore Courses for Railways exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup