Sin, Cos, and Tan

Aartt · 2010-12-14 14:17:22

why would it be tan? not sin or cos

bobbym · 2010-12-14 14:20:25

Because you are looking for the opposite side ( height ) and you have the adjacent side to the angle 37°. So the only one is toa. Remember your sohcahtoa.
Okay, now this one is a little tougher, but in the beginning you did ask what are they used for.

Aartt · 2010-12-14 16:12:13

sooo the ajacent side measures 100 soo and the angle is 37 hmm so the opposite side length is 60.18 right and to find the hypotanuse i use the pythagian therom and soo 100²+37² = c² which is also 10,000+1369=11369² so the answer from me to the cat is 106.62 unit and the ground from the cat is 60.18 unit right?

Aartt · 2010-12-14 16:27:33

noo wait the opposite side is 75.56 unit and then 10,000+5709.31=125.34 soo the length between me and the cat is 125.34 unit and the cat from the ground is 75.56 ya

Aartt · 2010-12-14 16:29:14

oh so you use tan when you only know one length and one angle and the length is not the hypotenuse and sin and cos when you know the hypotonuse right. correct me if im wrong

bobbym · 2010-12-14 16:32:26

Hi;

Yes, you use what you have in relation to sohcahtoa. Here we have an angle and the side adjacent to it, we need the side opposite the angle Only one relation, tangent for this one.

I am going to take a little break to eat see you in a bit.

Aartt · 2010-12-14 16:49:35

kk so i got the question right?

bobbym · 2010-12-14 17:09:53

Yes, can you answer the question of how high my cat is? My ladder is 80 feet tall and I would hate to carry it down there if it is not tall enough.

Aartt · 2010-12-14 17:14:36

yep you wouldnt waste your time taking the ladder out

bobbym · 2010-12-14 17:15:48

How do you know?

Aartt · 2010-12-14 17:24:00

because the opposite side of the right triangle is 75.56 unit high and the ladder is 80 units high right?

bobbym · 2010-12-14 17:27:56

Oh wait, my back just went out so the ladder is out. My brother is putting a plank from where I am standing to the cat. It is exactly as long as the hypotenuse. How long is the plank?

Aartt · 2010-12-14 17:29:28

the plank is 125.34 units long

bobbym · 2010-12-14 17:32:20

That is a little long. Looking at your height calculation, that is a little bit to high also. Please check you height again.

Aartt · 2010-12-14 17:38:14

ook
umm is it 123.33 ?

bobbym · 2010-12-14 17:39:48

Hi Aartt;

That is not right, let me see what you are doing. I really do need to see your work otherwise I cannot figure out what happened.

Hi Bob;

Looks like you are busier now than before you retired. Looks like you are happy.

I agree about staying off the streets. First comes the long hair and freaky clothes then comes the partying. Then the women start chasing you. Pretty soon your a major celeb. Avoid that life at all costs.

Bob · 2010-12-15 01:07:50

Hi bobbym,

I never knew about the

women start chasing you

!!:)!!

Maybe I should re-consider my life-plan.

Now about this cat.

Is the adjacent still 100ft and the angle 37. Because I then make it hypotenuse = 125.2ft.

Hint for you and Aartt.

(i) bobbym. Post a fresh diagram so Aart can see what you're giving for each problem.

(ii) Aartt Say whether you are using SOH, CAH or TOA each time, then exactly what calculation you are doing, finally your answer.

That way it will be clear where you are going wrong. (or hopefully, not going wrong at all! )

Bob

Last edited by Bob (2010-12-15 01:18:18)

Aartt · 2010-12-15 02:26:41

ook im using i think toa because i dont really know and maybe my thing for finding the hypotenuse isnt really a formula maybe i made a mistake or im not even sure it is a formula because im not that good with geometery but thanks bundy for the H=Adj/cos(angle) and i think bundy has answered the question not me well just another failed assingement in life

Bob · 2010-12-15 04:55:41

hi Aartt,

Don't be depressed about it. MIF help will get you there!

This is how I get my students to do these:

(i) Check you have got a right angled triangle. (In our exams it's common to give an isosceles triangle. The students must cut it down the line of symmetry before they can use trig.)

(ii) Decide what you know: angle? adjacent? opposite? hypotenuse? and what you are asked to calculate.

(iii) Choose SOH, CAH or TOA as appropriate.

(iv) Decide the exact form of the formula.

(v) Substitute numbers and find the required value.

(vi) Consider, 'is this a sensible value for this problem?'

Here's an example:

See diagram below.

(i) Yes, it has a right angle.
(ii) I know Adjacent and Hypotenuse and want the angle.
(iii) I'll use CAH
(iv) So

(v) so

so x = 36.9

(vi) 8 is not too far under 10 so the angle is probably under 45. 36 seems reasonable.

Would you like to try this one:

see second diagram

Bob

Last edited by Bob (2010-12-15 04:59:08)

Aartt · 2010-12-15 12:09:15

sooo im gonna do your problem bob bundy but i dont get what the 3 significant figures is .. first i did 1.9/3.2 and i got 0.59 then i clicked the tan -¹ because i only know the adjacent and the opposite.. and i got with the tan -¹ 30.54 soo the angle x is equal to 30.54°. Right? correct me if im wrong.

Aartt · 2010-12-15 12:13:01

and just wondering. so you use the tan-¹, or the cos-¹, or the sin-¹ when your trying to find the angle of something? right?

Aartt · 2010-12-15 17:07:57

hello? plz tell me if im right

Bob · 2010-12-15 22:44:53

hi Aartt,

You'll notice a big time difference between our posts. My clock is saying that you posted at 5.07 GMT. I'm in Essex, England, so I was tucked up in bedy-byes at that time. I've only just logged in to MIF (10.30 GMT). Sorry for the delay, but this is going to happen as our posts fly around the world.

Your method is exactly right and your answer so well done!

3 sf means three significant figures. This exam board says that because they don't want students copying 8 or 10 digits off their calculators and because it tests their ability to round off answers sensibly.

So to 3 sf the division should be 0.594. Then I left the full digit value in my calculator and did the inverse tangent to get 30.69972255 which I rounded to 30.7

I notice your answer is a little below this. That's because you did the inverse tangent of a figure that was already rounded. That leads to a minor inaccuracy. (inv tan 0.59 = 30.54) Best practice is to leave the full set of figures in your calc. at each stage even if you write down a rounded answer. That way you preserve maximum accuracy throughout. But this is a minor point; the great thing is you applied the right method!

At the bottom is another one to try:

Bob

Aartt · 2010-12-16 03:55:56

ok thanks for the tip bob bundy ok so now on to the question. im gonna use cah for this one because im trying to find the opposite ok but first i need to find what length the adjacent side is so i do (on the calculator) cos(40)*10 and got 7.66. so the adjacent side must be 7.66 cm. now to find the opposites length. because im using cah im gonna do 7.66/10 then click cos-¹ oh wait then i go back to 40 XD let me correct myself oh wait uhhh now im stuck but i think that the opposite is 7.66 why do i forget things so easily
(undeveloped brain?, too much info is stored in it in such a young age?)

Bob · 2010-12-16 07:29:39

hi Aartt,

You know H = 10, and the angle.

You want to find 'O'.

So you should be using SOH.

Do you want to try again from there?

Bob

Math Is Fun Forum

#51 2010-12-14 14:17:22

Re: Sin, Cos, and Tan

#52 2010-12-14 14:20:25

Re: Sin, Cos, and Tan

#53 2010-12-14 16:12:13

Re: Sin, Cos, and Tan

#54 2010-12-14 16:27:33

Re: Sin, Cos, and Tan

#55 2010-12-14 16:29:14

Re: Sin, Cos, and Tan

#56 2010-12-14 16:32:26

Re: Sin, Cos, and Tan

#57 2010-12-14 16:49:35

Re: Sin, Cos, and Tan

#58 2010-12-14 17:09:53

Re: Sin, Cos, and Tan

#59 2010-12-14 17:14:36

Re: Sin, Cos, and Tan

#60 2010-12-14 17:15:48

Re: Sin, Cos, and Tan

#61 2010-12-14 17:24:00

Re: Sin, Cos, and Tan

#62 2010-12-14 17:27:56

Re: Sin, Cos, and Tan

#63 2010-12-14 17:29:28

Re: Sin, Cos, and Tan

#64 2010-12-14 17:32:20

Re: Sin, Cos, and Tan

#65 2010-12-14 17:38:14

Re: Sin, Cos, and Tan

#66 2010-12-14 17:39:48

Re: Sin, Cos, and Tan

#67 2010-12-15 01:07:50

Re: Sin, Cos, and Tan

#68 2010-12-15 02:26:41

Re: Sin, Cos, and Tan

#69 2010-12-15 04:55:41

Re: Sin, Cos, and Tan

#70 2010-12-15 12:09:15

Re: Sin, Cos, and Tan

#71 2010-12-15 12:13:01

Re: Sin, Cos, and Tan

#72 2010-12-15 17:07:57

Re: Sin, Cos, and Tan

#73 2010-12-15 22:44:53

Re: Sin, Cos, and Tan

#74 2010-12-16 03:55:56

Re: Sin, Cos, and Tan

#75 2010-12-16 07:29:39

Re: Sin, Cos, and Tan

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