How Can Ken use Similar Triangles to find the height of a Building?

Question

Ken is 6 Feet Tall and his Shadow is 10 Feet long. The shadow of the Building is 25 Feet Long.

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Answer 1 · 2018-04-27T04:37:07

The height of the building is #=AB=15# ft.

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Triangles #DeltaABC# and #DeltaDEC# are similar trianglesbecause all three of their corresponding angles are congruent.

Therefore, the ratios of their corresponding sides are equal.

#(AB)/(DE)=(BC)/(EC)#

#(AB)/6=(BC)/10#

Let's solve for #BC#:

#BC=10/6(AB)=5/3(AB)#

#BC=25# ft. (shadow of the building)

Let's plug it in:

#25=5/3(AB)#

#AB=25/(5/3)=25*3/5=15# ft.