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Refer to the graphic novel frame below. The brochure says that the rope is 500 feet long. Jacob drew a triangle in the sand that is similar to the actual triangle formed by a parasailer and the boat. Use the properties of similar triangles to determine the parasailer's height above

Refer To The Graphic Novel Frame Below The Brochure Says That The Rope Is 500 Feet Long Jacob Drew A Triangle In The Sand That Is Similar To The Actual Triangle class=

Sagot :

   To solve this problem use the property of similar triangles,

 "Corresponding sides of the similar triangles are proportional"

By using this property, height of the parasailer is 160 feet.

From the figure attached,

  • In ΔPQR, a parasailer is a at point P and a boat is at R.
  • Actual length of the rope PR = 500 ft
  • Jacob drew a similar triangle ABC in which parasailer is at A and the boat is at C.

Let the height (PQ) of the parasailer = x ft

Height of the parasailer AB = 25 ft.

And the length of the rope AC = 2.5 ft.

Since, both the triangles ΔABC and ΔPQR are the similar triangles, their corresponding sides will be proportional.

[tex]\frac{AB}{PQ}=\frac{AC}{PR}[/tex]

[tex]\frac{2}{x} =\frac{2.5}{200}[/tex]

[tex]x=\frac{200\times 2}{2.5}[/tex]

[tex]x=160[/tex] ft

        Therefore, height of the parasailer is 160 feet.

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