G.SRT-Mathematical Proportions/Similarities in Real Life

 

Common Core State Standard

CCSS.MATH.CONTENT.HSG.SRT.A.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

In order to find the height of the palm tree, a person must create a similar triangle triangle in relation to the tree itself.  A person must look at the top of a  tree and line it up to the sun.  Once this has been established, a person must measure the length of the trees shadow, their own shadow, and the height of the person.  The picture below is an example of how to create similar triangles.

Similar Triangles for Height

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