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From the top of a building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building?
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Given:
- Height of the building = 100 meters
- Angle of elevation of the top of the tower = 60 degrees
- Angle of depression of the base of the tower = 45 degrees
To find:
- Height of the tower
- Distance on the ground from the building to the tower
Approach:
We can use trigonometric ratios such as sine, cosine, and tangent to solve this problem. Since we have the angle of elevation and depression, we can use the tangent ratio to find the height of the tower and the distance on the ground.
Steps to find the height of the tower:
1. Draw a diagram to visualize the problem. Label the height of the building as 'h' and the height of the tower as 'x'.
2. From the top of the building, draw a line to the top of the tower. This forms a right-angled triangle with the base as 'x' and the height as 'h + x'.
3. According to the given information, the angle of elevation is 60 degrees. Therefore, we can write the following equation:
tan(60°) = (h + x) / x
4. Simplifying the equation:
√3 = (h + x) / x
√3x = h + x
√3x - x = h
(√3 - 1)x = h
x = h / (√3 - 1)
5. Substitute the value of 'h' as 100 meters:
x = 100 / (√3 - 1)
x ≈ 100 / (1.732 - 1)
x ≈ 100 / 0.732
x ≈ 136.36 meters
Steps to find the distance on the ground:
1. Draw a diagram to visualize the problem. Label the distance on the ground as 'd'.
2. From the top of the building, draw a line to the base of the tower. This forms a right-angled triangle with the base as 'd' and the height as 'x'.
3. According to the given information, the angle of depression is 45 degrees. Therefore, we can write the following equation:
tan(45°) = x / d
4. Simplifying the equation:
1 = x / d
d = x
d = 136.36 meters
Conclusion:
- The height of the tower is approximately 136.36 meters.
- The distance on the ground from the building to the tower is approximately 136.36 meters.
- Height of the building = 100 meters
- Angle of elevation of the top of the tower = 60 degrees
- Angle of depression of the base of the tower = 45 degrees
To find:
- Height of the tower
- Distance on the ground from the building to the tower
Approach:
We can use trigonometric ratios such as sine, cosine, and tangent to solve this problem. Since we have the angle of elevation and depression, we can use the tangent ratio to find the height of the tower and the distance on the ground.
Steps to find the height of the tower:
1. Draw a diagram to visualize the problem. Label the height of the building as 'h' and the height of the tower as 'x'.
2. From the top of the building, draw a line to the top of the tower. This forms a right-angled triangle with the base as 'x' and the height as 'h + x'.
3. According to the given information, the angle of elevation is 60 degrees. Therefore, we can write the following equation:
tan(60°) = (h + x) / x
4. Simplifying the equation:
√3 = (h + x) / x
√3x = h + x
√3x - x = h
(√3 - 1)x = h
x = h / (√3 - 1)
5. Substitute the value of 'h' as 100 meters:
x = 100 / (√3 - 1)
x ≈ 100 / (1.732 - 1)
x ≈ 100 / 0.732
x ≈ 136.36 meters
Steps to find the distance on the ground:
1. Draw a diagram to visualize the problem. Label the distance on the ground as 'd'.
2. From the top of the building, draw a line to the base of the tower. This forms a right-angled triangle with the base as 'd' and the height as 'x'.
3. According to the given information, the angle of depression is 45 degrees. Therefore, we can write the following equation:
tan(45°) = x / d
4. Simplifying the equation:
1 = x / d
d = x
d = 136.36 meters
Conclusion:
- The height of the tower is approximately 136.36 meters.
- The distance on the ground from the building to the tower is approximately 136.36 meters.
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From the top of a building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building?
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From the top of a building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building? 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 building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building? 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 building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building?.
From the top of a building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building? 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 building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building? 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 building hundred metre high the angle of elevation of the top of a tower is found to be 60 degree and the angle of depression of the base of the tower is 45 degree find the height of the tower and its distance on the ground from the building?.
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