Finding Missing parts??

misheeru · 2010-02-18 10:35:50

ok so im in geometry but my teacher thought we could handle some "basic" trigg problems and im hoplessly lost!

l = I need to find both Z and Y. i thought i new what i was doing however it is a multiple choice problem
l Y = and all the answers i came up with were not the choices. My choices are 37 39 and 51.
l = X <------- this is looks similar to the one im doing (hope it helps) so you can see that both Y and Z are on the
10 l = on the inside. Im really stumped and i drag at math so any help is REALLY appreciated!
l =
l =
l_ =
l_l________Z_=
8

Devantè · 2010-02-18 10:52:55

x = √(8²+10²) = √164 = 12.8 (3 s.f.)

As for the answers, use the tangent rule twice;

Angle Y: arctan(8/10) = 38.66° (probably 39° by your choices)

Angle Z: arctan(10/8) = 51.34° (also could have simply used the 180° rule of triangles)

If you didn't understand what I did above: remember SOHCAHTOA? Sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent? Well, these can also be applied to angles too; you have to use the inverse trig functions (arcsin, arccos, arctan - sometimes denoted sin[sup]-1[/sup], cos[sup]-1[/sup], tan[sup]-1[/sup], or asin, acos, atan - in order to find the angles.

For Angle Y: 8 is opposite the angle Y, so it is my OPPOSITE side. Adjacent to that is 10, and it couldn't possibly be the hypotenuse because we know that it would be opposite the right-angle in this case. So if tan = opposite/adjacent, then tan(Y) = 8/10... we have to take the inverse tangent of both sides.

If you still need further help on this topic, I will make a video on my YouTube channel.

misheeru · 2010-02-18 11:10:31

k i have another one only this time its a rectangular solid.
The given is that l=8, W=4 and H= 2. I need to find the diagonal... which in this case is d. and the answer is written as:
d= √ then the answer.

oh and P.S thankyouX10000 devante'!

Last edited by misheeru (2010-02-18 11:12:03)

Devantè · 2010-02-18 11:21:15

Sometimes questions like that can be hard to imagine, so imagine in our rectangular solid we want to find the diagonal on the bottom of the solid. To do that, we need the length and the width (8 and 4) - by Pythagoras' Theorem, a² + b² = c²;

8² + 4² = c²
80 = c²
Square rooting both sides;
√80 = c

At this point, don't calculate that square root - you'll need the most precise possible value in order to complete the problem. Now that we have the diagonal that runs along the bottom, we can use that to find the diagonal that connects the two opposite corners in the rectangular solid that you are referring to. Here's why they gave us the height - 2. We use Pythagoras' Theorem again;

a² + b² = c²

2² + √80² = d²
4 + 80 = 84 (because the square root of something squared means they'll cancel out !)
d = √84

So the solution to the problem is that the diagonal is √84. If this is hard to picture in your head (which it is usually for most people without paper) then I can provide a video if need be.

misheeru · 2010-02-18 11:35:44

ok so i understand the a² + b² = c² thing a little better when i come to two numbers like 8²+10²... but what do you do if you only have 1 number to work with? Or like a number and the degrees of an angle?

l =
l =
l = 8
X l =
l =
l =
l_ =
l_l______ 20 _=
Y <------ Like here. Btw thats 20 degrees. In this situation im supposed to be finding both X and Y and rounding them to the nearest 10th. And like my first question its multiple choice and none of my ansers match up. -_- the options are: 2.7, 2.9 and 7.5.

bobbym · 2010-02-18 12:17:45

Hi misheeru;

Do you know about SOHCAHTOA?

Hint: I like 2.7 for X and 7.5 for Y

misheeru · 2010-02-18 12:26:03

kay and thankyou for your help!

bobbym · 2010-02-18 12:30:47

Hi misheeru;

Hold it! Don't you want to see how I did it?

misheeru · 2010-02-18 12:32:20

lol yes that would help.. i have more problems like those (three pages) *Sob*

bobbym · 2010-02-18 12:37:38

Hi;

You use the mnemonic SOHCAHTOA. Sine of your angle = Opposite side / Hypotenuse. That's how you remember these basic relations.

Sin(20° ) = X / 8

.34202 = X / 8

X = .34202 * 8

X = 2.73616 rounding to the nearest tenth = 2.7

misheeru · 2010-02-18 12:40:28

ok ill try and remember that thanx

bobbym · 2010-02-18 12:41:33

Hi;

And for Y. What do you do there?

misheeru · 2010-02-18 13:16:48

well since its the hypoteneuse/opposite do you start with
the Sin(20° ) = Y/X instead of using the 8 like you did when it was X?

bobbym · 2010-02-18 13:22:09

Hi;

No, we use the second part of the mnemonic; CAH which says Cosine of the angle equals Adjacent / Hypotenuse

Cos(20°) = Y / 8

.93969 = Y / 8

Y = .93969 * 8

Y = 7.51752 rounded to the nearest tenth = 7.5

Good signature by the way. Serious people die young or have bad stomachs.

misheeru · 2010-02-18 13:58:38

hence my father lol...
this must be a hassle but do you think u could put a few more examples of the mnuemonic<-----idk if thats spelled right) i mean like some more problems and steps to solving them (im asking you to come up with the problems of yours, that way ur nor doing my homework for me

bobbym · 2010-02-18 14:12:38

Hi misheeru;

(im asking you to come up with the problems of yours, that way ur nor doing my homework for me

An interesting assignment. You see, I didn't do my own homework when it mattered so now I do other peoples homework? Since usually 58% of my answers are incorect that is my revenge.

OK, I have no life anyway. We need to find x in the drawing of the right triangle at the bottom of this post.

We have from the mnemonic
The Sine of the Angle we know = The Opposite side to the angle over the Hypotenuse.
This one doesn't apply, because we don't know what h is yet. The next one is
The Cosine of the Angle we know = The Adjacent side (the side next to the angle) over the Hypotenuse. Again we don't know what h is.
The last one:
The Tangent of the Angle we know = The Opposite side to the angle over the Adjacent side. This relation works because we have 2 out of the 3 quantittes.

Tan(41°) = x / 16

.86928 = x / 16

x = 16 * .86928 = 13.90848 = 13.9 rounded to the nearest tenth.

Now you have 2 sides of that right triangle, compute the hypotenuse to the nearest tenth. you try it.

bobbym · 2010-02-18 14:30:21

I am going to eat now and watch Hoffa, when I get back I would like to see your work.

misheeru · 2010-02-18 14:32:25

geezus u tryin to kill me?!
mmkay so from here we start with the sine of the angle?

misheeru · 2010-02-18 14:46:29

kay since you gone ima just give it a try and u can tell me wut i got wrong and how to fix it...
attempt:

Sine(41°) = H / 13.9

.86928 = H / 13.9

H = 13.9 * .86928 = 12.082992 rounded to 12.1
there's my try

bobbym · 2010-02-18 22:45:19

Hi misheeru;

Glad that you tried.

Remember the mnemonic:
SOHCAHTOA

Sine of the angle = side Opposite the angle over the Hypotenuse. So your equation is:

Sin(41°) = 13.908 / h

.65605 = 13.908 / h

h = 13.908 / .65605

h = 21.1996037 = 21.2 rounded to the nearest tenth.

Do you see where you went wrong?

Devantè · 2010-02-19 05:43:26

misheeru wrote:

k i have another one only this time its a rectangular solid.
The given is that l=8, W=4 and H= 2. I need to find the diagonal... which in this case is d. and the answer is written as:
d= √ then the answer.

In case my solution wasn't clear, I created a video;

http://www.youtube.com/watch?v=tSuD5a6rf38 (the example used is the problem you gave me)

If you need a bit of a re-cap on Pythagoras' Theorem, you might want to see my other video;

http://www.youtube.com/watch?v=vS_fbzvPtmU

I will also be creating sine, cosine and tangent videos, where I'll show in detail how to find angles and sides in right-angled triangles using sine, cosine and tangent. I'll also move on to 3-D trigonometry if you're interested, which is more of a GCSE topic.

EDIT: I have just created another video on the sine rule. You can see it here;

http://www.youtube.com/watch?v=DWKpQ4l94v8

It contains two examples of problems that I made up. I will include harder examples later, and more videos using the cosine and tangent rules, along with the inverse trig functions.

PS: Sorry for the terrible handwriting, I had to use a mouse.

Last edited by Devantè (2010-02-19 06:53:08)

Devantè · 2010-02-19 11:05:19

Here's another video I made later on the cosine rule;

http://www.youtube.com/watch?v=m7_WaHlLIr4

View at your own leisure!

Math Is Fun Forum

#1 2010-02-18 10:35:50

Finding Missing parts??

#2 2010-02-18 10:52:55

Re: Finding Missing parts??

#3 2010-02-18 11:10:31

Re: Finding Missing parts??

#4 2010-02-18 11:21:15

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#5 2010-02-18 11:35:44

Re: Finding Missing parts??

#6 2010-02-18 12:17:45

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#7 2010-02-18 12:26:03

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#8 2010-02-18 12:30:47

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#9 2010-02-18 12:32:20

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#10 2010-02-18 12:37:38

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#11 2010-02-18 12:40:28

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#12 2010-02-18 12:41:33

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#13 2010-02-18 13:16:48

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#14 2010-02-18 13:22:09

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#15 2010-02-18 13:58:38

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#16 2010-02-18 14:12:38

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#17 2010-02-18 14:30:21

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#18 2010-02-18 14:32:25

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#20 2010-02-18 22:45:19

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