Question

Question 155

Points A and B are on the opposite edges of a pond as shown in the given 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, $\Delta ADC$ is a right angled triangle
In right angled $\Delta ADC$, by Pythagoras theorem,
$(AC{)}^2=(AD{)}^2+(CD{)}^2$
$\Rightarrow (AC{)}^2=(30{)}^2+(40{)}^2$ [$\because$ AD = 30 cm and CD = 40 cm, given]
$\Rightarrow (AC{)}^2=900+1600\Rightarrow (AC{)}^2=2500\Rightarrow AC=\sqrt{2500}\therefore AC=50m$
Now, AB = AC - BC = 50 - 12 = 38 m
Hence, the distance AB is 38 m