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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?
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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.
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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?
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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?.
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