Question

Need help with 3 quick multiple choice questions-- [Questions Inside]

Answer 1

@zepdrix

Answer 2

Oh special triangles, these aren't too bad.

Answer 3

Remember your rule for 45/45/90?
The hypotenuse should be the length of the shorter side, times sqrt2.

Answer 4

long leg = 6√(3)
short leg = 6
hypotenuse = 12

Answer 5

Whenever you see a sqrt(3),
know that they're `probably` referring to a 30/60/90 triangle.

Let's verify to make sure though.

In a 30/60/90 triangle:
`longest side` is twice the length of the `shortest side`.
The 12 side is twice the 6 side, ok good so far.

Also in a 30/60/90,
the `medium side` is \(\rm \sqrt{3}\) times the length of the `shortest side`.

Answer 6

Were you able to figure out the first one based on the info I gave you? :o
And the second one?

Answer 7

would the first one be 8sqrt3?

Answer 8

@zepdrix

Answer 9

..?

Answer 10

Quoting myself:
`Remember your rule for 45/45/90?`
`The hypotenuse should be the length of the shorter side, times sqrt2.`

Answer 11

I thought it would be 8sqrt2 or 16 ?

Answer 12

The shorter side, 8, times sqrt(2).
So 8sqrt(2). Yes.

Answer 13

No.\[\large\rm 8\sqrt2\ne8\cdot2\]

Answer 14

okay thats what I thought 8sqrt2 or 16 but its 8sqrt2 right

Answer 15

What about the other two now?

Answer 16

For number two,
there is no sqrt(2) showing up anywhere,
so we clearly don't have a 45/45/90 triangle as we did before.

Answer 17

When you see a sqrt(3), know that it's `probably` a 30/60/90 triangle.
I verified it above if you need to see the steps.

So yes, it's a 30/60/90 triangle in problem two.

Answer 18

ok so C for two. What about number 3? What do you think?

Answer 19

Recall that for a 45/45/90,
to go `from the short side` `to the long side`, we multiplied by sqrt(2).

This one is going to be a little trickier.
To go `from the long side` `back to the short side`, we divide by sqrt(2).

So the length x is going to be \(\large\rm \dfrac{10}{\sqrt2}\)

Answer 20

But that's one of our options, ya?

Answer 21

So we need to rationalize this.
Multiply top and bottom by sqrt(2),\[\large\rm \frac{10\sqrt{2}}{\sqrt{2}\sqrt{2}}\quad=\frac{10\sqrt2}{2}\quad=5\sqrt{2}\]If those steps are too confusing for you,
another way to think of it...

When you go from the short side to the long side, `multiply by sqrt(2).`
When you go from the long side back to the short side, `cut your number in half, and multiply by sqrt(2).`

Answer 22

Thank you zepdrix