Class 10 Exam > Class 10 Questions > Angle of depression of boat from a 50m high B...
Start Learning for Free
Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is?
Verified Answer
Angle of depression of boat from a 50m high Bridge is 30 degree then t...
Let the height of the bridge be “x” metres = 50 m
Let the distance between the bridge and the boat be “y” metres
Angle of depression is 30 degrees
=> angle of elevation form boat to the highest point of the bridge = 30 degrees
Tan 30 degrees = height of the bridge / distance between bridge and boat
=> (1 / √3) = x / y
=> 1 / √3 = 50 / y
=> y = 50√3
Distance of the boat from the bridge is 50√3 = 50 * 1.73 = 86.5 metres
Let the distance between the bridge and the boat be “y” metres
Angle of depression is 30 degrees
=> angle of elevation form boat to the highest point of the bridge = 30 degrees
Tan 30 degrees = height of the bridge / distance between bridge and boat
=> (1 / √3) = x / y
=> 1 / √3 = 50 / y
=> y = 50√3
Distance of the boat from the bridge is 50√3 = 50 * 1.73 = 86.5 metres
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
Angle of depression of boat from a 50m high Bridge is 30 degree then t...
The problem involves calculating the horizontal distance of a boat from a bridge, given the height of the bridge and the angle of depression.
Understanding the Scenario
- A bridge is 50 meters high.
- The angle of depression from the top of the bridge to the boat is 30 degrees.
Using Trigonometry
To solve for the horizontal distance (let’s call it "d") from the base of the bridge to the boat, we can use basic trigonometric concepts. The angle of depression is equal to the angle of elevation from the boat to the top of the bridge due to alternate interior angles.
Identifying the Right Triangle
- The height of the bridge (opposite side) = 50 meters.
- The angle of elevation = 30 degrees.
- The horizontal distance (adjacent side) = d.
Using the tangent function:
Formula
- The tangent of an angle in a right triangle is given by:
tan(θ) = opposite / adjacent
Substituting the values:
tan(30°) = 50 / d
Calculating d
- We know that tan(30°) = 1/√3 or approximately 0.577.
Thus, we set up the equation:
1/√3 = 50 / d
Solving for d
Cross-multiplying gives:
d = 50 * √3
- Using √3 ≈ 1.732:
d ≈ 50 * 1.732 ≈ 86.6 meters
Conclusion
Therefore, the horizontal distance of the boat from the bridge is approximately 86.6 meters.
Understanding the Scenario
- A bridge is 50 meters high.
- The angle of depression from the top of the bridge to the boat is 30 degrees.
Using Trigonometry
To solve for the horizontal distance (let’s call it "d") from the base of the bridge to the boat, we can use basic trigonometric concepts. The angle of depression is equal to the angle of elevation from the boat to the top of the bridge due to alternate interior angles.
Identifying the Right Triangle
- The height of the bridge (opposite side) = 50 meters.
- The angle of elevation = 30 degrees.
- The horizontal distance (adjacent side) = d.
Using the tangent function:
Formula
- The tangent of an angle in a right triangle is given by:
tan(θ) = opposite / adjacent
Substituting the values:
tan(30°) = 50 / d
Calculating d
- We know that tan(30°) = 1/√3 or approximately 0.577.
Thus, we set up the equation:
1/√3 = 50 / d
Solving for d
Cross-multiplying gives:
d = 50 * √3
- Using √3 ≈ 1.732:
d ≈ 50 * 1.732 ≈ 86.6 meters
Conclusion
Therefore, the horizontal distance of the boat from the bridge is approximately 86.6 meters.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
|
Explore Courses for Class 10 exam
|
|
Top Courses for Class 10View all
Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is?
Question Description
Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is?.
Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is?.
Solutions for Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? defined & explained in the simplest way possible. Besides giving the explanation of
Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is?, a detailed solution for Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? has been provided alongside types of Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? theory, EduRev gives you an
ample number of questions to practice Angle of depression of boat from a 50m high Bridge is 30 degree then the horizontal distance of a Boat from the bridge is? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 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