# At 11 A.M., a 5-foot post casts a 3- foot shadow. At the same time, a tree casts a shadow that is 21 feet in length. What is the height of the tree?

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Assuming that the pole and tree form right angles with the ground, the sysytems of the pole and shadow and tree and shadow form similar right triangles. (The right angles are congruent, and the angle of inclination from the end of the shadow to the top of the pole/tree are the same.)

Then the following ratio is true:

`5/3=x/21` (where x is the height of the tree.) Using the means-extremes product property we get:

`3x=105 ==> x=35`

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**The tree is 35 feet tall**.

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Let a 5-foot post stand normal to the ground i.e post is perpendicular to the ground.So tip of the post ,tip of shadow and foot of the post form a right angle triangle. If we consider shadow as base then altitude is hieght of the post. Let similar assumption for treee,its shadow and foot of the tree. Thus tree,its shadow also form a right angle triangle . **These two triangle are similar because angle of elevation of the tip of the post and tree are equal at 11 a.m. ** Since triangles are similar therefore corresponding sides are in proportion.

height of post/ length of shadow of post=height of tree/length of shadow of the tree

Let height of the tree be=x

`5/3=x/21`

`x=(21xx5)/3=35 ` feet