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From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine the height of the tower.?
Most Upvoted Answer
From the top of a 7 metre high building the angle of elevation of the ...
Understanding the Problem
To determine the height of the cable tower, we will use the angles of elevation and depression from the top of the building. The building is 7 metres high.
Visual Representation
- Let "A" be the top of the building.
- Let "B" be the foot of the cable tower.
- Let "C" be the top of the cable tower.
- The angle of elevation from A to C is 60 degrees.
- The angle of depression from A to B is 45 degrees.
Using Trigonometry
1. Height of the Foot of the Tower (B):
- The angle of depression to point B is 45 degrees.
- Since the height of the building (A) is 7 metres and the angle of depression is 45 degrees, we can use the tangent function:
- Height from A to B = 7 metres (height of building) = distance from A vertically down to B.
2. Finding the Height of the Tower (C):
- The angle of elevation to point C (the top of the tower) is 60 degrees.
- The height from A to C can be calculated using the tangent function:
- Let the height of the tower (C) be "h". The relationship is:
- tan(60 degrees) = h / x, where x is the horizontal distance from A to the base of the tower at B.
- Recalling that tan(60 degrees) = √3, we have h = √3 * x.
3. Combining the Heights:
- The total height (C) of the tower from the ground (B) is given by:
- Total height (C) = Height of the building (A) + Height of tower (h).
- Therefore, height of the tower = (h + 7) meters.
Conclusion
- Calculate the total height to determine the exact height of the cable tower above the ground.
- This approach effectively combines geometry and trigonometry to solve the problem accurately.
To determine the height of the cable tower, we will use the angles of elevation and depression from the top of the building. The building is 7 metres high.
Visual Representation
- Let "A" be the top of the building.
- Let "B" be the foot of the cable tower.
- Let "C" be the top of the cable tower.
- The angle of elevation from A to C is 60 degrees.
- The angle of depression from A to B is 45 degrees.
Using Trigonometry
1. Height of the Foot of the Tower (B):
- The angle of depression to point B is 45 degrees.
- Since the height of the building (A) is 7 metres and the angle of depression is 45 degrees, we can use the tangent function:
- Height from A to B = 7 metres (height of building) = distance from A vertically down to B.
2. Finding the Height of the Tower (C):
- The angle of elevation to point C (the top of the tower) is 60 degrees.
- The height from A to C can be calculated using the tangent function:
- Let the height of the tower (C) be "h". The relationship is:
- tan(60 degrees) = h / x, where x is the horizontal distance from A to the base of the tower at B.
- Recalling that tan(60 degrees) = √3, we have h = √3 * x.
3. Combining the Heights:
- The total height (C) of the tower from the ground (B) is given by:
- Total height (C) = Height of the building (A) + Height of tower (h).
- Therefore, height of the tower = (h + 7) meters.
Conclusion
- Calculate the total height to determine the exact height of the cable tower above the ground.
- This approach effectively combines geometry and trigonometry to solve the problem accurately.
Community Answer
From the top of a 7 metre high building the angle of elevation of the ...
7(√3+1)
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From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine the height of the tower.?
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From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine 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 From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine 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 From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine the height of the tower.?.
From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine 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 From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine 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 From the top of a 7 metre high building the angle of elevation of the top of a cable tower is 60 degree and the angle of depression of its foot is 45 degree determine the height of the tower.?.
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