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Castroville Street and Vindale Avenue intersect. If the diagonal distance across the intersection is 10 meters and Castroville Street is 8 meters wide, how wide is Vindale Avenue?

Respuesta :

Answer:

The length of Vindale Avenue = x = AB = 6 m

Step-by-step explanation:

Given data

Diagonal distance AC = 10 m

BC = length of castroville Street = 8 m

Let  the length of Vindale Avenue = x

Thus a Δ ABC is formed.

From the Δ ABC

[tex]AC^{2} = AB^{2} + BC^{2}[/tex]

[tex]10^{2} = x^{2} + 8^{2}[/tex]

[tex]x^{2} = 100 - 64[/tex]

[tex]x^{2} = 36[/tex]

x = 6 m

Therefore the length of Vindale Avenue = x = AB = 6 m

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