Question

Kelsey is 5 feet tall and stands 35 feet away from the building and she cast a shadow 8 feet long find the height of the building

Answer 1

`x=21.875=21.9\ ft`

Explanation:

Given:

AB = h = x = height of building

DE = 5 ft Kelsey tall

AD = 35 ft

DC = 8 ft

To Find:

AB = h = x = height of building

Solution

In Δ ABC and Δ DEC

∠A ≅ ∠D …………..{ measure of each angle is 90° given }

∠B ≅ ∠E .............. AB

∠C ≅ ∠C ……….....{Reflexive Property}

Δ ABC ~ Δ DEC ….{Angle-Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

`(AB)/(DE) =(BC)/(EC) =(AC)/(CD)\ \textrm{corresponding sides of similar triangles are in proportion}\\`

On substituting the given values we get

`(x)/(5) =(35)/(8)`

`x=21.875=21.9\ ft`