Shyam 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 design an ingenious way to overcome this difficulties. First, he fixes a pole at a convenient point o So that from O,both ends are visible. Then he fixes another pole at a point D on line A O such that AO= DO.In a similar way, he fixes a thirdpole at pt. C of line BO such that BO=CO.Then he measures CD and find that CD=170cm .prove that distance between objects A and B us also 170m
Since vertex O is common to both triangles OCD and OAB, you have SAS to show that the two triangles are congruent, making CD and AB congruent.
To prove that the distance between objects A and B is also 170 cm, we can make use of the similarity of triangles AOC and BOD.
Let's consider the triangles AOC and BOD.
Since AO = DO and BO = CO, we have:
AO = DO
BO = CO
Now, let's apply the property of similar triangles to triangles AOC and BOD.
Since angle AOC is common to both triangles and angles DOB and COA are right angles:
∠AOC = ∠DOB (corresponding angles)
∠DOA = ∠COB (right angles)
Therefore, triangles AOC and BOD are similar.
Now, let's look at the sides of the triangles. We know that CD = 170 cm.
Since the triangles are similar, we have the following ratios:
AO/BO = DO/CO
Since AO = DO and BO = CO, the ratios simplify to:
1 = 1
This shows that AO/BO = DO/CO = 1.
So, the lengths of the corresponding sides are also equal:
AO = DO
BO = CO
Since AO = DO, this implies that the distance between objects A and B, which is represented by AB, is equal to 170 cm:
AB = 170 cm
Therefore, we have proven that the distance between objects A and B is also 170 cm.