Chapter 8.4, Problem 20PSB

Solution

To Calculate: The length of S’s Shadow.

Length of S’s Shadow is $\frac{5.5}{4}$

Given information: S is $3$ ft. from a lamppost that is $12$ high.

Formula used: Here, we are using Angle Angle similarity.

Calculation: Here, $DE\parallel BC$

And, In $\Delta DAE$ and $\Delta BAC$

  $\angle A=\angle A$ (common)

  $\angle ADE=\angle ABC$ (corresponding angles)

Hence, $\Delta DAE\sim \Delta BAC$ (by Angle Angle similarity)

So, $\frac{AE}{AC}=\frac{DE}{BC}$

Now, putting the values

➔ $\frac{AE}{3}=\frac{5.5}{12}$

➔ $AE=\frac{5.5}{4}$

Hence, Shadow is $\frac{5.5}{4}$ ft. long.