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Question
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
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Solution
Since, ΔACD is a right angled triangle.
In right angled ΔADC, by Pythagoras theorem,
(AC)2 = (AD)2 + (CD)2
⇒ (AC)2 + (30)2 + (40)2 ...[∵ AD = 30 cm and CD = 40 cm, given]
⇒ (AC)2 = 900 + 1600
⇒ (AC)2 = 2500
⇒ AC = `sqrt(2500)`
∴ AC = 50 m
Now, AB = AC – BC = 50 – 12 = 38 m
Hence, the distance AB is 38 m.
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