Answered

IDNLearn.com provides a comprehensive platform for finding accurate answers. Our experts provide prompt and accurate answers to help you make informed decisions on any topic.

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
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.