Railways Exam > Railways Questions > Two trees are standing along the opposite sid...
Start Learning for Free
Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?
- a)200
- b)200√3
- c)100√3
- d)250
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Two trees are standing along the opposite sides of a road. Distance be...
In the figure, H is the height of the other tree.
In triangle AEB, AB = 200/tan45°
⇒ AB = 200 mtr
⇒ BC = 400 - 200 = 200 mtr
In triangle DCB, tan 60° = H/BC
⇒ H = 200√3 mtr
∴ Height (in metres) of the other tree = 200√3 mtr
Most Upvoted Answer
Two trees are standing along the opposite sides of a road. Distance be...
And 60 degrees. Let's call the height of the first tree h1 and the height of the second tree h2.
Using the given angles of depression, we can form two right triangles. The first triangle consists of the first tree, the point, and the line connecting the first tree to the point. The second triangle consists of the second tree, the point, and the line connecting the second tree to the point.
In the first triangle, the angle of depression is 45 degrees. This means that the angle opposite to the line connecting the first tree to the point is also 45 degrees. Since the angle opposite a 45-degree angle in a right triangle is also 45 degrees, the first triangle is an isosceles right triangle.
Similarly, in the second triangle, the angle of depression is 60 degrees. This means that the angle opposite to the line connecting the second tree to the point is also 60 degrees. Since the angle opposite a 60-degree angle in a right triangle is also 30 degrees, the second triangle is a 30-60-90 triangle.
Now, let's analyze each triangle separately:
First Triangle (45-45-90):
Since the first triangle is isosceles, the two legs of the triangle are congruent. Let's call the length of each leg x. The hypotenuse of the triangle will be 400 - x (as the distance between the trees is 400 meters). In a 45-45-90 triangle, the ratio of the lengths of the legs to the hypotenuse is 1:1:√2.
So, in this triangle, we have:
h1 = x
400 - x = x√2
Simplifying the second equation:
400 = x(√2 + 1)
400/√2 + 400 = x
Therefore, h1 = x = 400/√2 + 400 ≈ 850.85 meters.
Second Triangle (30-60-90):
In a 30-60-90 triangle, the ratio of the lengths of the sides opposite to the angles is 1:√3:2.
In this triangle, we have:
h2 = x√3 (since the line connecting the second tree to the point is opposite the 60-degree angle)
400 - x = 2x√3 (since the line connecting the second tree to the point is opposite the 30-degree angle)
Simplifying the second equation:
400 = 2x√3 + x
400 = x(2√3 + 1)
400/(2√3 + 1) = x
Therefore, h2 = x√3 = 400/(2√3 + 1) ≈ 275.77 meters.
So, the height of the first tree (h1) is approximately 850.85 meters and the height of the second tree (h2) is approximately 275.77 meters.
Using the given angles of depression, we can form two right triangles. The first triangle consists of the first tree, the point, and the line connecting the first tree to the point. The second triangle consists of the second tree, the point, and the line connecting the second tree to the point.
In the first triangle, the angle of depression is 45 degrees. This means that the angle opposite to the line connecting the first tree to the point is also 45 degrees. Since the angle opposite a 45-degree angle in a right triangle is also 45 degrees, the first triangle is an isosceles right triangle.
Similarly, in the second triangle, the angle of depression is 60 degrees. This means that the angle opposite to the line connecting the second tree to the point is also 60 degrees. Since the angle opposite a 60-degree angle in a right triangle is also 30 degrees, the second triangle is a 30-60-90 triangle.
Now, let's analyze each triangle separately:
First Triangle (45-45-90):
Since the first triangle is isosceles, the two legs of the triangle are congruent. Let's call the length of each leg x. The hypotenuse of the triangle will be 400 - x (as the distance between the trees is 400 meters). In a 45-45-90 triangle, the ratio of the lengths of the legs to the hypotenuse is 1:1:√2.
So, in this triangle, we have:
h1 = x
400 - x = x√2
Simplifying the second equation:
400 = x(√2 + 1)
400/√2 + 400 = x
Therefore, h1 = x = 400/√2 + 400 ≈ 850.85 meters.
Second Triangle (30-60-90):
In a 30-60-90 triangle, the ratio of the lengths of the sides opposite to the angles is 1:√3:2.
In this triangle, we have:
h2 = x√3 (since the line connecting the second tree to the point is opposite the 60-degree angle)
400 - x = 2x√3 (since the line connecting the second tree to the point is opposite the 30-degree angle)
Simplifying the second equation:
400 = 2x√3 + x
400 = x(2√3 + 1)
400/(2√3 + 1) = x
Therefore, h2 = x√3 = 400/(2√3 + 1) ≈ 275.77 meters.
So, the height of the first tree (h1) is approximately 850.85 meters and the height of the second tree (h2) is approximately 275.77 meters.
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
|
|
Similar Railways Doubts
Top Courses for RailwaysView all
Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer?
Question Description
Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct 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 Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct 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 Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer?.
Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct 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 Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct 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 Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer?.
Solutions for Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct 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 Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angles of depression of the point from the top of the trees are 45° and 60°. If the height of the tree which makes 45° angle is 200 metres, then what will be the height (in metres) of the other tree?a)200b)200√3c)100√3d)250Correct 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