Class 10 Exam > Class 10 Questions > On a straight line passing through the foot o...
Start Learning for Free
On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower?
Most Upvoted Answer
On a straight line passing through the foot of a tower,two point C and...
Community Answer
On a straight line passing through the foot of a tower,two point C and...
Given Information:
- There is a tower.
- Two points C and D are on a straight line passing through the foot of the tower.
- The distance between the foot of the tower and point C is 4m.
- The distance between the foot of the tower and point D is 16m.
- The angles of elevation from C and D to the top of the tower are complementary.
To Find:
- The height of the tower.
Assumptions:
- We assume that the ground is flat and the tower is vertical.
Solution:
Step 1: Drawing a Diagram:
- Draw a straight line representing the ground.
- Mark a point for the foot of the tower.
- Label this point as A.
- Mark points C and D on the straight line passing through A.
- Label point C as C and point D as D.
- Draw vertical lines from points C and D to represent the tower.
- Label the top of the tower as T.
Step 2: Establishing Relationships:
- Let h be the height of the tower.
- From the given information, we can establish the following relationships:
- AC = 4m
- AD = 16m
- Angle CAT + Angle DAT = 90 degrees (as the angles of elevation from C and D to the top of the tower are complementary)
Step 3: Applying Trigonometry:
- We can use trigonometry to solve for the height of the tower.
- In right triangle ACT, we have:
- tan(angle CAT) = h/AC = h/4
- In right triangle ADT, we have:
- tan(angle DAT) = h/AD = h/16
Step 4: Solving the Equations:
- Since the angles of elevation are complementary, we have:
- tan(angle CAT) = cot(angle DAT)
- Equating the expressions for tangent from step 3:
- h/4 = 16/h
- Cross-multiplying and simplifying:
- h^2 = 64
- Taking the square root of both sides:
- h = 8m
Step 5: Final Answer:
- The height of the tower is 8 meters.
- There is a tower.
- Two points C and D are on a straight line passing through the foot of the tower.
- The distance between the foot of the tower and point C is 4m.
- The distance between the foot of the tower and point D is 16m.
- The angles of elevation from C and D to the top of the tower are complementary.
To Find:
- The height of the tower.
Assumptions:
- We assume that the ground is flat and the tower is vertical.
Solution:
Step 1: Drawing a Diagram:
- Draw a straight line representing the ground.
- Mark a point for the foot of the tower.
- Label this point as A.
- Mark points C and D on the straight line passing through A.
- Label point C as C and point D as D.
- Draw vertical lines from points C and D to represent the tower.
- Label the top of the tower as T.
Step 2: Establishing Relationships:
- Let h be the height of the tower.
- From the given information, we can establish the following relationships:
- AC = 4m
- AD = 16m
- Angle CAT + Angle DAT = 90 degrees (as the angles of elevation from C and D to the top of the tower are complementary)
Step 3: Applying Trigonometry:
- We can use trigonometry to solve for the height of the tower.
- In right triangle ACT, we have:
- tan(angle CAT) = h/AC = h/4
- In right triangle ADT, we have:
- tan(angle DAT) = h/AD = h/16
Step 4: Solving the Equations:
- Since the angles of elevation are complementary, we have:
- tan(angle CAT) = cot(angle DAT)
- Equating the expressions for tangent from step 3:
- h/4 = 16/h
- Cross-multiplying and simplifying:
- h^2 = 64
- Taking the square root of both sides:
- h = 8m
Step 5: Final Answer:
- The height of the tower is 8 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
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower?
Question Description
On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? 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 On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower?.
On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? 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 On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower?.
Solutions for On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? 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 On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? defined & explained in the simplest way possible. Besides giving the explanation of
On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower?, a detailed solution for On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? has been provided alongside types of On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? theory, EduRev gives you an
ample number of questions to practice On a straight line passing through the foot of a tower,two point C and D are at distance of 4m and 16m from the foot respectively. If the angels af elevation from C and D of the top of the tower are complementary, then find the height of the tower? 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