Question

What is the distance d across the lake?

Answer 1

The distance d across the lake is 90ft.

Solution-

In the picture,

ΔABC ≈ ΔCDE

Because,

1. ∠ACB = ∠DCE (∵ vertical opposite angles)
2. ∠B = ∠D = 90°
3. ∠ACB = ∠CED (∵ as other two angles are same and sum of those two angles when subtracted from 180° will result the same)

So, from similarity properties

`\Rightarrow (AB)/(DE)=(BC)/(DC)`

`\Rightarrow (120)/(20)=(d)/(15)`

`\Rightarrow d=(120* 15)/(20)=90`