Answer:
176.39 inches or
14.70 feet
Step-by-step explanation:
Consider the right triangle made by Kristen, ground and shadow.
This triangle has one leg as 64 inches.
Next consider the right triangle formed by street light, ground upto shadow tip.
The two triangles have common angle of elevation and also another angle as 90 degrees.
Hence the two triangles would be similar
Also if A is the angle made by hypotenuse of both triangles with the ground we have
[tex]tanx=\frac{64}{82}[/tex]
This value also equals by bigger triangle as
[tex]tanx=\frac{h}{82+12(12)}=\frac{h}{226}[/tex]
From these two we get
h = height of street light =[tex]\frac{226(64)}{82} =176.39[/tex]
