Question

A meter stick casts a shadow 2.4 m long at the same time a flagpole casts a shadow 9.7 m long. How tall is the flagpole

Answer 1

The first thing we are going to do is draw a diagram of the situation to help us to solve the situation.
We an draw tow similar triangle between the length of the shadows and the height of the stick and the pole.
Since meter stick has a length of 1 meter, the height of our smaller triangle is 1 meter. Let $h$ be height of of the pole. Since both triangles are similiar we can establish a proportion between their corresponding sides and solve for $h$:
$\frac{h}{1} = \frac{9.7}{2.4}$
$h=\frac{9.7}{2.4}$
$h=4.04$

We can conclude that the pole is 4.04 meters tall.