Question

What is the distance d across the lake?

Answer 1

Answer-

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

$\Rightarrow \dfrac{AB}{DE}=\dfrac{BC}{DC}$

$\Rightarrow \dfrac{120}{20}=\dfrac{d}{15}$

$\Rightarrow d=\dfrac{120\times 15}{20}=90$