Algebra Word Problem involving Similar Triangles

[afritts1987]

You are hiking along the California coast and wonder about the height of a particular Giant Redwood tree. You are 5 feet and nine inches tall and your shadow is 11 feet long. The shadow of the tree is 407 feet long. How tall is the tree?

I know that I'm suppose to draw two similar triangles. The base of the first triangle is 11 and the base of the other triangle is 407. The height of the first triangle is gonna be the height of the person. But from there on I'm stuck.......how do I solve this?

 

[mmm4444bot]

Hello Afritts:

Pick a variable name for the height of the tree, like h, and label the height of the second triangle h.

The length of this side is what you're trying to figure out because h will tell you the height of the tree.

Now you have four sides. Write an equation. The equation is a proportion (i.e., two ratios set equal to one another).

The ratios can both be height:base, or you could go with height:height = base:base.

~ Mark

 

[Denis]

With similar triangles, ratios of corresponding sides are equal;
thus you simply need to solve: x / 407 = 5.75 / 11
x = height of tree

 

[mmm4444bot]

... or you could go with height:height = base:base.

Which makes Denis' equation x/5.75 = 407/11

Good grief ... I'm beginning to quote myself ...

 

[Denis]

... or you could go with height:height = base:base.
Which makes Denis' equation x/5.75 = 407/11

Good grief ... I'm beginning to quote myself ...

HEE HAW