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.

Answer 1

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.