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a 34 foot tree casts a 53 foot shadow what is the distance from the top of the tree to the far shadow

Sagot :

Answer:

62.97ft

Step-by-step explanation:

Pythagorean Theorem

When the two side lengths of a right triangle are given and we need to know the side length of the other side, we can use the Pythagorean Theorem to compute it!

                                             [tex]a^2+b^2=c^2[/tex],

where a and b are the legs of the triangle and c is the hypotenuse.

This equation can be rearranged to find each side length:

  • [tex]c=\sqrt{a^2+b^2}[/tex]
  • [tex]b=\sqrt{c^2-a^2}[/tex]
  • [tex]a=\sqrt{c^2-b^2}[/tex]

[tex]\hrulefill[/tex]

Solving the Problem

Visualizing the Problem

We're told

  • a tree has a height of 34 ft
  • casts a shadow on the ground--adjacent to the tree--of length 53 ft

and we need to find the distance from the tip of the shadow to the top of the tree.

An image of a right triangle can be drawn to model this:

  • the vertical leg representing the tree's height or 34ft
  • the horizontal leg representing the length of the shadow or 53 ft
  • the hypotenuse representing the distance we need to find.

(See the image attached).

[tex]\dotfill[/tex]

Solving for the Distance

We're given the a and b parts of the theorem's equation, all we do is plug and calculate for the hypotenuse or the distance.

                                         [tex]c=\sqrt{34^2+53^2}[/tex]

                                         [tex]c=\sqrt{3965}[/tex]

                                         [tex]c=62.97[/tex]

So, the distance between the tip of the shadow and the top of the tree is 62.97ft.

View image Zarahaider4211
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