Question

Kristen is 64 inches tall, and she stands 12 feet away from a streetlight. If she casts an 82-inch-long shadow, how tall is the streetlight rounded to the nearest hundredth of a foot?

Answer 1

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

$tanx=\frac{64}{82}$

This value also equals by bigger triangle as

$tanx=\frac{h}{82+12(12)}=\frac{h}{226}$

From these two we get

h = height of street light =$\frac{226(64)}{82} =176.39$