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A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall?
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A ladder rests against a vertical such that the top of the ladder reac...
Length of the Ladder and Height of the Wall:
Given:
- The ladder is inclined at 60° with the ground.
- The bottom of the ladder is 1.5m away from the foot of the wall.
Finding the Length of the Ladder:
- The ladder, the wall, and the ground form a right-angled triangle.
- The angle between the ladder and the ground is 60°.
- The distance between the bottom of the ladder and the foot of the wall is the base of the triangle.
- The length of the ladder is the hypotenuse of the triangle.
- Using trigonometry, we can use the sine function to find the length of the ladder.
- sin(60°) = height of the wall / length of the ladder.
- height of the wall = length of the ladder * sin(60°).
- Substitute the given values to find the length of the ladder.
Finding the Height of the Wall:
- To find the height of the wall, we can use the Pythagorean theorem.
- The height of the wall is the side opposite the angle of 60° in the right-angled triangle.
- Using the Pythagorean theorem, we have (length of the ladder)^2 = (height of the wall)^2 + (1.5m)^2.
- Substitute the length of the ladder value to find the height of the wall.
Conclusion:
- The length of the ladder is calculated using trigonometry, and the height of the wall is found using the Pythagorean theorem. Make sure to substitute the given values correctly and perform the calculations accurately to find the length of the ladder and the height of the wall.
Given:
- The ladder is inclined at 60° with the ground.
- The bottom of the ladder is 1.5m away from the foot of the wall.
Finding the Length of the Ladder:
- The ladder, the wall, and the ground form a right-angled triangle.
- The angle between the ladder and the ground is 60°.
- The distance between the bottom of the ladder and the foot of the wall is the base of the triangle.
- The length of the ladder is the hypotenuse of the triangle.
- Using trigonometry, we can use the sine function to find the length of the ladder.
- sin(60°) = height of the wall / length of the ladder.
- height of the wall = length of the ladder * sin(60°).
- Substitute the given values to find the length of the ladder.
Finding the Height of the Wall:
- To find the height of the wall, we can use the Pythagorean theorem.
- The height of the wall is the side opposite the angle of 60° in the right-angled triangle.
- Using the Pythagorean theorem, we have (length of the ladder)^2 = (height of the wall)^2 + (1.5m)^2.
- Substitute the length of the ladder value to find the height of the wall.
Conclusion:
- The length of the ladder is calculated using trigonometry, and the height of the wall is found using the Pythagorean theorem. Make sure to substitute the given values correctly and perform the calculations accurately to find the length of the ladder and the height of the wall.
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A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall?
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A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall? 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 A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall?.
A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall? 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 A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall?.
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A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall?, a detailed solution for A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall? has been provided alongside types of A ladder rests against a vertical such that the top of the ladder reaches the top of the wall.the ladder is inclined at 60• with the ground ,and the bottom of the ladder is 1.5m away from the foot of the wall.find( i)the length of the ladder,and (ii) the height of the wall? theory, EduRev gives you an
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