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Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling?
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Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicul...
Given:
- Height of the first pole (P1) = 30 feet
- Height of the second pole (P2) = 50 feet
- Distance between the poles = 40 feet
To find:
(i) The horizontal distance from the coupling point (C) to the taller pole (P2).
(ii) The height of the coupling point (C) above the ground.
(iii) The distance down the wire from the smaller pole (P1) to the coupling point (C).
Solution:
Step 1: Analyzing the Situation
Let's analyze the given situation and visualize it for better understanding.
- We have two poles, P1 and P2, with heights of 30 feet and 50 feet respectively.
- The poles are 40 feet apart and perpendicular to the ground.
- The wires supporting the poles are attached from the top of one pole to the bottom of the other.
- The coupling point C is where the two wires cross.
Step 2: Finding the Horizontal Distance from C to P2
To find the horizontal distance from the coupling point (C) to the taller pole (P2), we can use similar triangles.
- The two poles and the horizontal ground form a right-angled triangle.
- Let's consider the distance from the coupling point (C) to the base of the taller pole (P2) as x feet.
- The distance from the coupling point (C) to the base of the shorter pole (P1) would then be (40 - x) feet.
Using the property of similar triangles, we can write:
x / 30 = (40 - x) / 50
Cross-multiplying, we get:
50x = 30(40 - x)
Simplifying the equation, we get:
50x = 1200 - 30x
Adding 30x to both sides, we get:
80x = 1200
Dividing both sides by 80, we get:
x = 15
Therefore, the horizontal distance from the coupling point (C) to the taller pole (P2) is 15 feet.
Step 3: Finding the Height of the Coupling Point (C) above the Ground
To find the height of the coupling point (C) above the ground, we can consider the right-angled triangle formed by the taller pole (P2) and the horizontal distance from the coupling point (C) to P2.
Using the Pythagorean theorem, we can write:
(P2C)^2 = (PC)^2 + (P2P)^2
Substituting the values, we get:
(P2C)^2 = 15^2 + 50^2
(P2C)^2 = 225 + 2500
(P2C)^2 = 2725
Taking the square root of both sides, we get:
P2C = √2725
P2C ≈ 52.14
Therefore, the height of the coupling point (C) above the ground is approximately 52.14 feet.
Step 4: Finding the Distance down the Wire from P1 to C
To find the distance down the wire from the smaller pole (P1) to the coupling point (C), we can use similar triangles.
- Height of the first pole (P1) = 30 feet
- Height of the second pole (P2) = 50 feet
- Distance between the poles = 40 feet
To find:
(i) The horizontal distance from the coupling point (C) to the taller pole (P2).
(ii) The height of the coupling point (C) above the ground.
(iii) The distance down the wire from the smaller pole (P1) to the coupling point (C).
Solution:
Step 1: Analyzing the Situation
Let's analyze the given situation and visualize it for better understanding.
- We have two poles, P1 and P2, with heights of 30 feet and 50 feet respectively.
- The poles are 40 feet apart and perpendicular to the ground.
- The wires supporting the poles are attached from the top of one pole to the bottom of the other.
- The coupling point C is where the two wires cross.
Step 2: Finding the Horizontal Distance from C to P2
To find the horizontal distance from the coupling point (C) to the taller pole (P2), we can use similar triangles.
- The two poles and the horizontal ground form a right-angled triangle.
- Let's consider the distance from the coupling point (C) to the base of the taller pole (P2) as x feet.
- The distance from the coupling point (C) to the base of the shorter pole (P1) would then be (40 - x) feet.
Using the property of similar triangles, we can write:
x / 30 = (40 - x) / 50
Cross-multiplying, we get:
50x = 30(40 - x)
Simplifying the equation, we get:
50x = 1200 - 30x
Adding 30x to both sides, we get:
80x = 1200
Dividing both sides by 80, we get:
x = 15
Therefore, the horizontal distance from the coupling point (C) to the taller pole (P2) is 15 feet.
Step 3: Finding the Height of the Coupling Point (C) above the Ground
To find the height of the coupling point (C) above the ground, we can consider the right-angled triangle formed by the taller pole (P2) and the horizontal distance from the coupling point (C) to P2.
Using the Pythagorean theorem, we can write:
(P2C)^2 = (PC)^2 + (P2P)^2
Substituting the values, we get:
(P2C)^2 = 15^2 + 50^2
(P2C)^2 = 225 + 2500
(P2C)^2 = 2725
Taking the square root of both sides, we get:
P2C = √2725
P2C ≈ 52.14
Therefore, the height of the coupling point (C) above the ground is approximately 52.14 feet.
Step 4: Finding the Distance down the Wire from P1 to C
To find the distance down the wire from the smaller pole (P1) to the coupling point (C), we can use similar triangles.
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Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling?
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Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling? 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 Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling?.
Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling? 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 Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling?.
Solutions for Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the horizontal distance from C to the taller pole? ii) How high above the ground is the coupling? (iii)How far down the wire from the smaller pole is the coupling? in English & in Hindi are available as part of our courses for Class 10.
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