Angelina has a lawn, ABCD. She has placed a watering hose, BD, as shown below.
Part A: Angelina plans to put a fence along the length AD of her lawn. What is the length of the fence required?
Part B: Using complete sentences, explain how you arrived at the answer for Part A.

- anonymous

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- anonymous

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- Hero

Hi Katlovesmath94

- anonymous

hahah hey :)

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- Hero

I'll let outkast explain since he is so eager

- anonymous

can you help me with this? I am not sure where to start and I am suppose to explain it

- anonymous

ok thanks

- anonymous

For the triangle BCD you are given two of the sides and you can use Pythagorean's theorem to find the third side, the length of side BD. Once you have that, side BD and the 60-degree angle given can be used in a trig function (sine, cosine, or tangent -- which one?) to find out the length of side AD.

- anonymous

soooo I am still confused what am I doing?

- anonymous

Step one: look at the triangle BCD. You are given two sides, correct? Let's find the third side, BD. How do we find the third side of a right triangle? Using Pythagorean's theorem. Are you familiar with Pythagorean's theorem? a^2 + b^2 = c^2 ?

- anonymous

yes

- anonymous

what am I putting in the pathagoreum therum formula

- anonymous

|dw:1343004042674:dw|

- Hero

Looks like a good explanation going on here so far.

- anonymous

There are 3 sides in a triangle. You are given two of them: 35 ft and 12 ft. Pythagorean's theorem \[a ^{2}+b ^{2}=c ^{2}\] means you can take those two sides you already know and plug them into "a" and "b" then solve for "c." Try it out. What do you get?

- anonymous

"c" here is just a generic variable, like x. In your picture, "c" represents the side BD of the triangle. So if you solve for c, you've solved for the length of side BD.

- anonymous

Do you got it? Or are you still confused on how to use the theorem to get the length of side BD?

- anonymous

no I am still lost not gonna lie I have been working on this for twenty minutes and I am not sure what I am doing

- anonymous

like I tried the pathegorium thing and I got some rediculas numbers in the thousands

- anonymous

I am just frustrated with this problem

- anonymous

When you got the large numbers had you already taken the square root of the number?

- anonymous

no i just did the pathagorium thing squared them and then what i have two huge number equal to c^2

- anonymous

what are you plugging in for Pythagoras theorem?

- anonymous

the 35 and 12

- anonymous

alright that's good. You are doing the right thing.
\[12^2+35^2=c^2\]\[144+1225=c^2\]\[1369=c^2\]

- anonymous

now square root both sides....what do you get then?

- anonymous

37?

- anonymous

Good job! So c = 37 means the length of side BD in your picture is 37 feet.

- anonymous

We are done with triangle BCD. Now look at the next triangle, ABD.

- anonymous

You are given one angle and one side. We can use a trig function to solve for side AD, which is what you need.

- anonymous

tan60

- anonymous

Perfect. Do you know the trick to remember the trig functions, SOH CAH TOA?
SOH: sin(angle)=opposite/hypotenuse
CAH: cos(angle)=adjacent/hypotenuse
TOA: tan(angle)=opposite/adjacent.

- anonymous

yes

- anonymous

So tan(60)=opposite/adjacent. What is the side that is opposite of the 60-degree angle? It's the side BD, which you just found out is 37 feet. And what is the side adjacent (or next to) the 60-degree angle? That's the one you're solving for, side AD. So
tan(60)=opposite/adjacent=60/AD
tan(60)=60/AD
Solve for AD. Do you know how to do that?

- anonymous

opposite is 35 but what is the adjacent? 37?

- anonymous

oh you multiply AD to both sides

- anonymous

The 35 is not the opposite side; that's the OTHER triangle; we aren't looking at that triangle at all anymore. We are looking for the opposite side of this small triangle ABD. The opposite of the 60-degree angle in that small triangle is the length BD. BD = 37 feet according to your calculation.

- anonymous

OH my bad, I mean tan(60)=37/AD

- anonymous

you still multiply AD to both sides right

- anonymous

tan(60) = opposite/adjacent = 37 / AD

- anonymous

Yes.

- anonymous

So multiplying both sides by AD gives you (AD) tan(60) = 37.
Then divide each side by tan(6), so you get AD = 37 / tan(60)

- anonymous

You should get something in the 20s for your answer for AD if you calculate the tan(60).

- anonymous

Does it make sense?

- anonymous

21.361

- anonymous

Perfect. Good job :)

- anonymous

If you practice problems like this over and over they get easier.

- anonymous

Sorry about a couple of my typos there.

- anonymous

thank goodness that is over lol sorry I was just frustrated I didnt understand how the big number in the pathagorium therum was working

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