Question

A 6​-ft vertical post casts a 10​-in shadow at the same time a nearby cell phone tower casts a 125​-ft shadow. How tall is the cell phone​ tower?A 6​-ft vertical post casts a 10​-in shadow at the same time a nearby cell phone tower casts a 125​-ft shadow. How tall is the cell phone​ tower?

Answer 1

Answer:

The height of cell phone tower is 75 ft.

Step-by-step explanation:

It is given that a 6​-ft vertical post casts a 10​-in shadow

The shadow of the cell phone tower is 125 ft.

Let the height of cell phone tower be "x" feet.

1 feet = 12 inches

Thus, shadow of vertical post is $\frac{10}{12} = \frac{5}{6} ft$

Since the time of day is same, the right angled triangles formed are similar.

Thus,

$\frac{x}{6} = \frac{125}{\frac{5}{6} }$

$x = \frac{(125)(36)}{5} = (25)(36) = 900 inches$

In feet, The height of the tower is $\frac{900}{12} = 75 ft$