If a tree 12 feet tall casts a shadow 50 feet long, how tall is a telephone pole that casts a shadow 75 feet long at the same time of the day?

Question

How would i set this problem up?

Answer 1

The set up is using similar triangles and then using a ratio and solving for x.

x

Because these triangles are similar they are in proportion and that means you can set up a ratio.

I wish I could draw here. The x is the height of the height of the telephone pole. The vertical line inside the major (larger) triangle is the height of the tree (12ft): they are in proportion. The bottom line is the length of the shadow cast by the telephone pole (75ft). The length of the shadow cast by the tree is 50ft and that begins from the left of the bottom line to the tree (the vertical line).

12ft/50ft = x/75ft

And, the rest is just algebra.

Answer 2

Use proportions to find the telephone pole length:

12ft tree/50ft shadow = Xft pole/75ft shadow

Cross-multiply to solve for X:

(12ft tree/50 ft shadow) * 75ft shadow = Xft pole

The pole is 18ft tall.