Respuesta :

Answer:

A)

[tex]\tt \cfrac{32}{x} =\cfrac{x}{18}[/tex]

[tex]\tt \sqrt{x^2} =\sqrt{576}[/tex]

[tex]\boxed {\tt x=24\:m}[/tex]

↑ (Parking lot from beach

B)

[tex]\tt \cfrac{32}{b} =\cfrac{b}{50}[/tex]

[tex]\tt \sqrt{b^2} =\sqrt{1600}[/tex]

[tex]\boxed{\tt b=40 \:m}[/tex]

↑ (Parking lot to the refreshment stand)

~

Answer:

a) 24 m

b) 40 m

Step-by-step explanation:

a) If an altitude is drawn to the hypotenuse of a right triangle, then the altitude is the geometric mean between the segments on the hypotenuse. Let x represent the altitude (the distance from the beach to the parking lot). Since we have similar triangles:

[tex] \frac{18}{x} = \frac{x}{32} [/tex]

[tex] {x}^{2} = 576[/tex]

[tex]x = 24[/tex]

b) Using the Pythagorean theorem, the distance from the beach to the replacement stand is

[tex] \sqrt{ {24}^{2} + {32}^{2} } = \sqrt{576 + 1024} = \sqrt{1600} = 40[/tex]

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