Question

Maura found that a redwood tree that is 32 yards tall casts a shadow 60 yards long. Then

Maura noticed that a cell phone tower nearby casts a shadow 45 yards long. How tall is the
cell phone tower?

Answer 1

By setting up a proportion using the known height and shadow length of a redwood tree and the shadow length of a cell phone tower, we find that the cell phone tower is 24 yards tall.

Step-by-step explanation:

The question is asking us to determine the height of a cell phone tower based on the shadow it casts, given that we know the height of a redwood tree and its shadow's length. This is a problem that can be solved using similar triangles, as both situations (the tree and the tower with their respective shadows) form right-angled triangles with the ground and their height as the two perpendicular sides.

To solve this, we can set up a proportion because the triangles are similar:

• The height of the redwood tree is 32 yards.
• The shadow of the redwood tree is 60 yards long.
• The shadow of the cell tower is 45 yards long.

We want to find the height of the cell tower (let's call it h).

So we have the proportion:

32 yards / 60 yards = h / 45 yards

By solving for h, we get:

h = (32 yards * 45 yards) / 60 yards = 24 yards

Therefore, the cell phone tower is 24 yards tall.