i need help ill just put the pic in the comment

Question

anonymous · Answer

attachment

mathstudent55 · Answer

This problem deals with a 30-60-90 triangle.

mathstudent55 · Answer

|dw:1408506104030:dw|

mathstudent55 · Answer

Are you familiar with the famous 30-60-90 triangle?

anonymous · Answer

not really, hope i don't seem dumb for asking, its cuz i got placed into advanced math and i have to figure this whole book out till summer ends so sorry

anonymous · Answer

no

mathstudent55 · Answer

Don't be sorry. You want to learn math. That's great.
I'll help you.

mathstudent55 · Answer

There are two famous right triangles that are used often in math.
For both of these triangles, the ratios of the lengths of the sides are known.
One such triangle is the 45-45-90 triangle.
The other one is the 30-60-90 triangle.

mathstudent55 · Answer

Let's go over the 30-60-90 triangle since this is what your problem deals with.

mathstudent55 · Answer

The name "30-60-90 triangle" comes from the measures of the angles. A 30-60-90 triangle has angles measuring 30 degrees, 60 degrees, and 90 degrees. Because of the 90-degree angle, which is a right angle, the 30-60-90 triangle is a right triangle.

mathstudent55 · Answer

Here is a 30-60-90 triangle.
|dw:1408506553825:dw|

mathstudent55 · Answer

The ratio of the lengths of the sides of a 30-60-90 triangle is:

$a : b : c = 1 : \sqrt 3 : 2$

mathstudent55 · Answer

Notice that   $a$   is the smallest side. It is opposite the smallest angle, 30 degrees. $a$ is the small leg.

$b$ is the large leg. It is opposite the 60-degree angle.

$c$ is the hypotenuse and the longest side of the triangle. It is opposite the 90-degree angle.

anonymous · Answer

yes

anonymous · Answer

i understand

mathstudent55 · Answer

From the ratio, you see that the hypotenuse is twice the length of the short leg.
Also, you see that the long leg is $\sqrt 3$ times longer than the short leg.

mathstudent55 · Answer

Now let's look at your problem.

mathstudent55 · Answer

You are given the length of the hypotenuse.
You are asked for the length of the long leg.

anonymous · Answer

yes

mathstudent55 · Answer

Use this statement first:
"From the ratio, you see that the hypotenuse is twice the length of the short leg."

Since the hypotenuse has length 24, what is the length of the SHORT leg?

anonymous · Answer

12?

anonymous · Answer

?

mathstudent55 · Answer

Correct.
The short leg measures 12.

Now we use the second statement:

"Also, you see that the long leg is $\sqrt 3$ times longer than the short leg."

The short leg measures 12.
The long leg is $\sqrt 3$ times longer than the short leg.
What is the length of the long leg?

anonymous · Answer

why do u put the square root sign

anonymous · Answer

cuz w/o sign if it was 3 x more then it would be 36

mathstudent55 · Answer

But it isn't 3 times longer.
It is sqrt(3) times longer.

anonymous · Answer

uh

anonymous · Answer

how do u calculate that?

anonymous · Answer

square root of 3 times longer of 12

mathstudent55 · Answer

I can show you how the ratios of the sides of the 30-60-90 triangle can be calculated.

mathstudent55 · Answer

Here's an equilateral triangle.
All sides have a length of 2.
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mathstudent55 · Answer

What are the angle measures of an equilateral triangle?

anonymous · Answer

uhm 60

mathstudent55 · Answer

Great.
Now we have this info on this triangle:

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So far so good?

anonymous · Answer

yup

mathstudent55 · Answer

Now we drop an altitude from the top vertex to the bottom side.
(Remember, an altitude is perpendicular to the opposite side.)

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mathstudent55 · Answer

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