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Question
If John wishes to determine the distance between two objects A and B, but there is an obstacle between the two objects which prevents him from making a direct measurement. He designed an ingenious way to overcome this difficulty. First, he fixes a pole at convenient point O so that from O, both ends are visible. Then he fixes another pole at a point on the line AO (produced) such that AO= DO. In a similar Way, he fixes a third pole at a point C on the line BO (produced) such that BO=CO. Then he measures CD and finds that CD = 170 cm. Find the distance between the objects A and B.
If John wishes to determine the distance between two objects A and B, but there is an obstacle between the two objects which prevents him from making a direct measurement. He designed an ingenious way to overcome this difficulty. First, he fixes a pole at convenient point O so that from O, both ends are visible. Then he fixes another pole at a point on the line AO (produced) such that AO= DO. In a similar Way, he fixes a third pole at a point C on the line BO (produced) such that BO=CO. Then he measures CD and finds that CD = 170 cm. Find the distance between the objects A and B.
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Solution
The correct option is B 170 cm
In ΔAOB and ΔCOD
AO=OD,BO=OC
∠AOB=∠COD (vertically opposite angles)
∴ ΔAOB≅ΔCOD ∴ AB=CD=170 cm
In ΔAOB and ΔCOD
AO=OD,BO=OC
∠AOB=∠COD (vertically opposite angles)
∴ ΔAOB≅ΔCOD ∴ AB=CD=170 cm
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