Question

Question #3063d

Answer 1

Check the method below.

Explanation:

Pythagorean's theorem states that in a right triangle, `a^2+b^2=c^2`, where `c` is your hypotenuse, or the angle opposite of the right angle, and `a` and `b` are either of your legs, or sides attached to the right angle.

For your first problem, you have both sides. Plug them into the theorem.

`3^2+3^2=c^2`
`9+9=c^2`
`18=c^2`
`sqrt(c^2)=sqrt(18)`
`c=sqrt(9)sqrt(2)`
`c=3sqrt(2)`

For your second problem, use the same theorem. However, note we're missing a leg and we have the hypotenuse already. Plug in accordingly.

`40^2+b^2=65^2`
`1600+b^2=4225`
`b^2=2625`
`b~~51.2`

Answer 2

`a^2+b^2=c^2`

Explanation:

Each of these problems uses the Pythagorean Theorem/Pythagoras' Theorem.

This theorem states that for a right angled triangle with hypoteneuse `c` and sides `a` and `b`, `a^2+b^2=c^2.` The hypoteneuse is the side opposite the right angle, and is always the longest side on a right angled triangle.

Example 1

For the first example, `a=3` and `b=3`.

`a^2+b^2=c^2`
`3^2+3^2=c^2`
`c^2=18`
At this point you can either take out your calculator to do `sqrt18`, or simplify the surd to get
`c=3sqrt2`

Example 2

For this problem, we need to re-arrange Pythagoras' theorem to make `a^2` the subject (because its neater to have squares than square roots and squares).

`a^2+b^2=c^2`
`a^2=c^2-b^2`
Now, we sub in our values
`a^2=65^2-40^2`
`a^2=4225-1600`
`a^2=2625`
Now using your calculator
`a=sqrt2625=5sqrt105~~51.2ft`