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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?

Shadow:

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.

Answer and Explanation:

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.


Learn more about this topic:

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Ratios and Proportions: Definition and Examples

from Geometry: High School

Chapter 7 / Lesson 1
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