Question

Please help! I don't know where to begin!

Answer 1

a) 24 m

b) 40 m

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:

`(18)/(x) = (x)/(32)`

`{x}^(2) = 576`

`x = 24`

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

`\sqrt{ {24}^(2) + {32}^(2) } = √(576 + 1024) = √(1600) = 40`

Answer 2

A)

`\tt \cfrac{32}{x} =\cfrac{x}{18}`

`\tt √(x^2) =√(576)`

`\boxed {\tt x=24\:m}`

↑ (Parking lot from beach

B)

`\tt \cfrac{32}{b} =\cfrac{b}{50}`

`\tt √(b^2) =√(1600)`

`\boxed{\tt b=40 \:m}`

↑ (Parking lot to the refreshment stand)

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