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A student wants to know how far above the ground the top of a leaning flagpole is. At high​ noon, when the sun is almost directly​ overhead, the shadow cast by the pole is 6 ft long. The student holds a plumb bob with a string 3 ft long up to the flagpole and determines that the point of the plumb bob touches the ground 14 in. from the base of the flagpole. How far above the ground is the top of the​ pole?

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pedrocarratore

Answer:

15.43 ft

Step-by-step explanation:

To solve this question, one should use the concept of similar triangles.

The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem.  Therefore, the distance of the top of the pole to the ground is:

[tex]14 in = 1.1667 ft[/tex]

[tex]1.1667x=6*3\\x = 15.43[/tex]

The distance of the top of the pole to the ground is 15.43 ft.

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