Answer:
[tex]x=21.875=21.9\ ft[/tex]
Step-by-step 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 ..............{corresponding angles ∵ DE || 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.
[tex]\frac{AB}{DE} =\frac{BC}{EC} =\frac{AC}{CD}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
On substituting the given values we get
[tex]\frac{x}{5} =\frac{35}{8}[/tex]
[tex]x=21.875=21.9\ ft[/tex]
