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a bluebird is sitting in her nest 10 feet up in a tree when she looks down and sees a cat and a worm. she decides to use math to determine if the cat is dar enough from the worm to gige hee time to fly down ans get the worm before the cat would read her. the worm is 7 feet from the base of the tree. how far is the cat from the worm?

the distance from the cat to the base of the tree is ___ feet (rounded to the nearest tenth)

the distance from the worm is ____ feet ( rounded to the nearest tenth).

Sagot :

Terence101

Answer:

12.2 feet

Step-by-step explanation:

The key to this problem is trigonometry.

Imagine a right triangle. With a height, 10 ft (representing the tree's height), and a base of 7 ft (representing the horizontal distance to the worm).

Now the hypoteneuse length, or otherwise the distance from the worm is unknown.

So this is where we can use the pythagorean theorem.

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

[tex]c[/tex] here is the hypoteneuse length, and [tex]a[/tex] and [tex]b[/tex] are the other lengths of the triangle.

Since we know a and b we can solve for c.

But first we will square root both sides of the equation to get [tex]c[/tex] and not  [tex]c^2[/tex].

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

Now just plug in our values for a and b respectively. (It doesn't matter what number replaces a or b, just make sure you are replacing a and b with the 2 known values) Calculate.

[tex]\sqrt{10^2 + 7^2} = \sqrt{100 + 49} = \sqrt{149} = 12.206....[/tex]

Round to the nearest tenth.

[tex]12.2[/tex] feet

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