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From the top of a vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.?
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From the top of a vertical tower, the angels of depression of two cars...
Understanding the Problem
We need to find the height of a vertical tower given the angles of depression to two cars positioned 100 m apart. The angles of depression are 45 degrees and 60 degrees.
Diagram Representation
- Let the height of the tower be "h".
- Place the tower at point T.
- Let the position of the car closer to the tower be point A and the other car be point B.
Using Trigonometry
1. Angle of Depression = 45 Degrees (Car A)
- In triangle TAH, where H is the point on the ground level directly beneath T:
- tan(45 degrees) = h / d1
- Since tan(45 degrees) = 1, we have:
- h = d1
2. Angle of Depression = 60 Degrees (Car B)
- In triangle TBH:
- tan(60 degrees) = h / d2
- Since tan(60 degrees) = √3, we have:
- h = d2 * √3
3. Distance Between the Cars
- d2 = d1 + 100 m (because they are 100 m apart).
Setting Up the Equation
- From the first equation: d1 = h.
- From the second equation: d2 = h / √3.
- Substitute d2 in the distance equation:
- h / √3 = h + 100.
Solving for Height
- Rearranging gives:
- h / √3 - h = 100.
- Factor out h:
- h(1/√3 - 1) = 100.
- Solving for h yields:
- h = 100 / (1/√3 - 1).
Final Calculation
After calculating, you will find the height of the tower. The final result will give you the answer in meters.
This method uses basic trigonometric principles to solve for the height of the tower efficiently.
We need to find the height of a vertical tower given the angles of depression to two cars positioned 100 m apart. The angles of depression are 45 degrees and 60 degrees.
Diagram Representation
- Let the height of the tower be "h".
- Place the tower at point T.
- Let the position of the car closer to the tower be point A and the other car be point B.
Using Trigonometry
1. Angle of Depression = 45 Degrees (Car A)
- In triangle TAH, where H is the point on the ground level directly beneath T:
- tan(45 degrees) = h / d1
- Since tan(45 degrees) = 1, we have:
- h = d1
2. Angle of Depression = 60 Degrees (Car B)
- In triangle TBH:
- tan(60 degrees) = h / d2
- Since tan(60 degrees) = √3, we have:
- h = d2 * √3
3. Distance Between the Cars
- d2 = d1 + 100 m (because they are 100 m apart).
Setting Up the Equation
- From the first equation: d1 = h.
- From the second equation: d2 = h / √3.
- Substitute d2 in the distance equation:
- h / √3 = h + 100.
Solving for Height
- Rearranging gives:
- h / √3 - h = 100.
- Factor out h:
- h(1/√3 - 1) = 100.
- Solving for h yields:
- h = 100 / (1/√3 - 1).
Final Calculation
After calculating, you will find the height of the tower. The final result will give you the answer in meters.
This method uses basic trigonometric principles to solve for the height of the tower efficiently.
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From the top of a vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.? for Class 10 2025 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 vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.?.
From the top of a vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.? for Class 10 2025 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 vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the top of a vertical tower, the angels of depression of two cars in the same straight line with the base of the tower, at an instant are found to be 45degree and 60 degree. If the cars are 100m apart on the same side of the tower, find the height of the tower.?.
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