Question

Standing 20 feet from a streetlight, a 5-foot tall woman casts an 8-foot shadow. How tall is the streetlight

Answer 1

Answer:

The height h of the streetlight is 17.5ft

$h=17.5ft$

Explanation:

The question can be illustrated in the drawing below;

Firstly, we need to find angle x;

$\begin{gathered} \tan x=\frac{5}{8} \\ x=\tan ^{-1}(\frac{5}{8}) \\ x=32^0 \end{gathered}$

From angle x we can now determine the value of height h of the streetlight;

$\begin{gathered} \tan x=\frac{h}{28} \\ \tan 32=\frac{h}{28} \\ h=28\times\tan 32 \\ h=28\times0.625 \\ h=17.5ft \end{gathered}$

The height h of the streetlight is 17.5ft

$h=17.5ft$