A pole that is 3.2m tall casts a shadow that is 1.47m long. At the same time, a nearby tower casts a shadow that is 37.25m long. How tall is the tower? Round your answer to the nearest meter.

Answer 1

Hi Samantha,

For this problem, the first step is to draw a picture. Notice that you have two triangles created by the two objects and their shadows.

The key here is that these two triangles are similar to each other. This is because the sun is shinning down at the same angle on each object, and so the angle created by the sun is the same for both triangles. So they have 1 congruent angle. Then you can notice that between both the pole and the ground, and the tower and the ground, it is a right angle. So we have 2 congruent angles. By Angle-Angle similarity criteria, these two triangles are similar.

When we have similar triangles, it means their sides are proportional. Therefore, we can set up a proportion setting the relationship of the heights equal to the relationships of the shadows:

Height of pole / height of tower = shadow from pole / shadow from tower

3.2 / height of tower = 1.47 / 37.25 (plugging in the values we know)

Next, we use cross multiplication to create the following equation:

3.2 * 37.25 = height of tower * 1.47

119.2 = height of tower * 1.47 (multiply 3.2 by 37.25)

height of tower = 81.0884 (divide both sides by 1.47)

Rounding to the nearest meter, our answer is that the height of the tower is 81 meters high.

I hope this helps. Let me know if you have any follow-up questions. Good luck!