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Points A and B are on the opposite edges of a pond as shown in 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 AADC, 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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