# Isaac is landscaping a yard, to see how well a tree shades the area of the yard. He needs to know...

## Question:

Isaac is landscaping a yard, to see how well a tree shades the area of the yard. He needs to know the tree's height. The tree's shadow is 18 feet long. At the same time, Isaac's shadow is 4 feet long. If Isaac is 6 feet tall, then how tall is the tree?

There are some shadows that have sharp edges and there are those that are rather blurred. The sharp edged shadows are formed when the light source is like a point-source or it comes from a single source. When the light source is wide, then the shadow will have softer edges.

The tree casts an 18-foot long shadow. Isaac's shadow is 4 feet long. Since Isaac is 6 feet tall, then the following ratio can be used to find the height of the tree, {eq}x {/eq}:

{eq}\begin{align} \rm \dfrac{x \ height \ of \ tree}{18 \ feet \ shadow} &= \rm \dfrac{6 \ feet \ Isaac's \ height}{4 \ feet \ shadow } \\ \dfrac x {18} &= \dfrac 6 4 \\ x &= \dfrac {(6)(18)} 4 \\ x &= 27 \end{align} {/eq}

The tree is {eq}\rm 27 \ feet {/eq} tall. 