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The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is?
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Given Information:
- Height of the tower = 100m
- Initial angle of elevation of the sun = 30°
- Final angle of elevation of the sun = 45°
Calculating the Length of the Shadow:
- Let x be the length of the shadow when the angle of elevation is 30°.
- Using trigonometry, tan(30°) = 100/x
- Solving for x, we get x = 100/tan(30°)
Calculating the New Length of the Shadow:
- Let y be the new length of the shadow when the angle of elevation is 45°.
- Using trigonometry, tan(45°) = 100/y
- Solving for y, we get y = 100/tan(45°)
Calculating the Difference:
- The difference in the lengths of the shadow is x - y.
- Substituting the values of x and y, we get x - y = 100/tan(30°) - 100/tan(45°)
Calculating the Value of x:
- Using the values of tan(30°) and tan(45°), we can calculate the value of x - y.
- After calculation, we find the value of x to be approximately 28.86 meters less.
Therefore, the value of x is approximately 28.86 meters less when the angle of elevation of the sun changes from 30° to 45°.
- Height of the tower = 100m
- Initial angle of elevation of the sun = 30°
- Final angle of elevation of the sun = 45°
Calculating the Length of the Shadow:
- Let x be the length of the shadow when the angle of elevation is 30°.
- Using trigonometry, tan(30°) = 100/x
- Solving for x, we get x = 100/tan(30°)
Calculating the New Length of the Shadow:
- Let y be the new length of the shadow when the angle of elevation is 45°.
- Using trigonometry, tan(45°) = 100/y
- Solving for y, we get y = 100/tan(45°)
Calculating the Difference:
- The difference in the lengths of the shadow is x - y.
- Substituting the values of x and y, we get x - y = 100/tan(30°) - 100/tan(45°)
Calculating the Value of x:
- Using the values of tan(30°) and tan(45°), we can calculate the value of x - y.
- After calculation, we find the value of x to be approximately 28.86 meters less.
Therefore, the value of x is approximately 28.86 meters less when the angle of elevation of the sun changes from 30° to 45°.
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The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is?
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The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is?.
The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height of a tower is 100m when the angle of elevation of the sun changes from 30° to 45° the shadow of the tower becomes x metres less the value of x is?.
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