Answer:
[tex]2.2 km[/tex]
Skills needed: Pythagorean Theorem
Step-by-step explanation:
1) We are given a right triangle. A right triangle has one right angle, which has a measure of 90 degrees.
- This theorem is used to find the side lengths of a right triangle. This problem is a perfect example for using this theorem.
------------------------------------------------------------------------------------------------------------- 2) Before using this theorem, there are some important vocab terms:
---> Legs: Legs are the two shorter sides of a right triangle. They are not opposite the right angle.
---> Hypotenuse: This is the side that is opposite of the right angle, and is also the longest side of the right triangle.
In the theorem below, [tex]a[/tex] and [tex]b[/tex] are the legs, [tex]c[/tex] is the hypotenuse
-------------------------------------------------------------------------------------------------------- 3) The theorem (essentially a formula) is:
[tex]a^2+b^2=c^2[/tex]
Now, let's determine which side is which variable:
- We are given [tex]a[/tex], which is 2, which is a leg.
- We are also given [tex]c[/tex], which is 3, which is the hypotenuse (since it is opposite of the right angle)
Let's plug it in below:
[tex]2^2+b^2=c^2[/tex], so we are solving for [tex]b[/tex], the other leg.
[tex]4+b^2=9[/tex] (simplifying the exponents)
[tex]b^2=5[/tex] (isolating the [tex]b[/tex] to solve)
[tex]b=\sqrt{5}[/tex] (square-rooting both sides to solve for "b")
[tex]b = \sqrt5=2.2[/tex]
square root 5 is rounded to 2.2, so that is the answer.
