Answer :
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.
