Answer-
The distance d across the lake is 90ft.
Solution-
In the picture,
ΔABC ≈ ΔCDE
Because,
- ∠ACB = ∠DCE (∵ vertical opposite angles)
- ∠B = ∠D = 90°
- ∠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
[tex]\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}[/tex]
[tex]\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}[/tex]
[tex]\Rightarrow d=\dfrac{120\times 15}{20}=90[/tex]
