Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the technique in the model above, find the missing side in this 30°-60°-90° right triangle.

Short = 5 , hypotenuse = 10
Long =

Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the technique in the model above, find the missing side in this 30°-60°-90° right triangle.



Short = 5 , hypotenuse = 10
Long =

mathstudent55 · Answer

You need to know the ratios of the lengths of the sides of a 30-60-90 triangle.

$1 : \sqrt 3 : 2$

mythorius · Answer

@KamiBug

mythorius · Answer

And @mathstudent55  That's confusing, math isn't my best subject

mathstudent55 · Answer

Ok. I'll explain.

mythorius · Answer

That would be nice, thank you.

mathstudent55 · Answer

As you can see in your drawing, a 30-60-90 triangle is a right triangle.
It has two legs, the sides that form the right angle, and a hypotenuse, the side opposite the right angle.

mathstudent55 · Answer

The legs are of different lengths.
The leg opposite the 30-degree angle is shorter than the leg opposite the 60-degree angle.

mathstudent55 · Answer

In addition, in a right triangle, the hypotenuse is always the longest side.

mathstudent55 · Answer

The three sides, in order of length, from shortest to longest are:
short leg, long leg, hypotenuse

mathstudent55 · Answer

Do you understand so far?

mythorius · Answer

Okay I understand the angles of triangles, I know a bit of geometry but this is tough for me.

mathstudent55 · Answer

Just read the above again.
So far it's pretty simple.
In a 30-60-90 triangle, the shortest side is the short leg (opposite the 30-deg angle).
Then the next longer side is the long leg (opposite the 60-deg angle).
The longest side is the hypotenuse (opposite the right angle).

mythorius · Answer

Okay. I know that. but the confusing part is the equation part. Not the triangle.

mythorius · Answer

Is it 5 (square root) 3?

mathstudent55 · Answer

Now that we know the order of the lengths of the sides, we can go one step further.
The lengths of the sides of a 30-60-90 triangle are in the ratio:

$1 : \sqrt 3 : 2$

If the shortest leg measures 1, then the hypotenuse measures 2.
That means the hypotenuse is twice the length of the short leg.
The long leg measures $\sqrt 3$. That means the long leg is $\sqrt 3$ times the length of the short leg.

mythorius · Answer

Yeah so the long leg would be 15. but what would the equation be? 5x^2+10x^2?

mathstudent55 · Answer

You are correct.
Since the4 short leg is 5, the long leg is $\sqrt 3$ time 5, so it is $5 \sqrt 3$

mythorius · Answer

Alright, that makes sense, thank you.

mathstudent55 · Answer

You can also use the Pythagoras theorem.

$a^2 + b^2 = c^2$

$5^2 + b^2 = 10^2$

$25 + b^2 = 100$

$b^2 = 75$

$b = \sqrt {75} $

$b = \sqrt {25 \times 3} $

$b = 5\sqrt 3$

mythorius · Answer

Can you help me with some more?

mathstudent55 · Answer

Sure.
Please start a new post for each new question.

mythorius · Answer

I know

mathstudent55 · Answer

You're welcome.