Question
Can you think of different methods to construct a 90° angle at a given point on a line using a rope?
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Answer
In this construction, we shall use the 3-4-5 principle that if the sides of a triangle are in the ratio 3 : 4 : 5, then the angle opposite to the longest side is 90°.
In the figure, the sides AB, BC, and CA are in the ratio 3 : 4 : 5 and the angle B, opposite to the longest side AC, is equal to 90°.
Construction:
Draw a line XY and take any point A on it.
We shall construct a 90° angle at point A, using a rope.
Fix a small pole at point A.
Take a rope and mark it at 0 units, 3 units, 8 units, and 12 units.
Attach the 0 unit mark and 12 unit mark of the rope at A.
Attach the 3-unit mark at point B on the line XY, with the help of a pole at B.
Now hold the 8-unit point of the rope and extend it away from XY so that both sides of this point are tight.
Place a pole at this point and call this point C, as shown in the figure.
In the ∆ABC, the sides are 3 units, 4 units, and 5 units.
The angle opposite to the longest side is ∠A.
∴ By the 3-4-5 principle, ∠A is equal to 90°.
∴ The line AC is perpendicular to the line XY at the given point A.
In the figure, the sides AB, BC, and CA are in the ratio 3 : 4 : 5 and the angle B, opposite to the longest side AC, is equal to 90°.
Construction:
Draw a line XY and take any point A on it.
We shall construct a 90° angle at point A, using a rope.
Fix a small pole at point A.
Take a rope and mark it at 0 units, 3 units, 8 units, and 12 units.
Attach the 0 unit mark and 12 unit mark of the rope at A.
Attach the 3-unit mark at point B on the line XY, with the help of a pole at B.
Now hold the 8-unit point of the rope and extend it away from XY so that both sides of this point are tight.
Place a pole at this point and call this point C, as shown in the figure.
In the ∆ABC, the sides are 3 units, 4 units, and 5 units.
The angle opposite to the longest side is ∠A.
∴ By the 3-4-5 principle, ∠A is equal to 90°.
∴ The line AC is perpendicular to the line XY at the given point A.
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