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. - Mathematics

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Sum

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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Chapter 6: Triangles - Exercise [Page 184]

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NCERT Exemplar Mathematics Class 7
Chapter 6 Triangles
Exercise | Q 155. | Page 184

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