Trigonometry question

Hi,

I have a question for an assignment that is giving me some trouble.

This is the question:

The diagram below shows part of the limpopo river where it is wide and straight. A tall fever tree, HT, stands vertically on one bank. An explorer who wants to find the height of the tree stands at pont A, on the bank directly opposite the tree, and measures the angle of elevation of its top, finding it to be 45 degrees.

He then walked 20 metres along the bank to the point B, and found that the angle of elevation of the tree from the bank was 30 degress.

Below I have created the same diagram.

If the width of the river, AT, is w metres:

i)Use traingle AHT to find HT in terms of w

ii) Use triangle HTB to find BT in terms of w

iii) use Pythagoros theorem in triangle ABT to write down the equation in w^2. Solve this equation, and thus find the height of the tree.

I'm experienced with Pythagoras theorem; sine, cosine, tangent; the sine rule and the cosine rule, but I do not feel that there are enough measurements for me to solve this.

This is an assignment question, so I do not want anyone to tell me the answer. I would just like some help and to be put in the right direction. I also need an explanation on what it means when it says "in terms of w

Thanks.

Also I have a question concerning cumlative frequency.

I have a question using grams, and it says that the weight is correct to the nearest gram. Does this mean I have to change the intervals?

The first two intervals are 85-89 and 90-94.

As the question is stating to the nearest gram do it change the intrervals to 84.5-89.5 and 89.5-94.5??

Thanks

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Reply 1

0x2a

For (i) and (ii) use SOHCAHTOA. In terms of w means you have to have in your final answer. For example wcos(87) = a or whatever.

For (iii), you know the length of AB, and you know that AT is w, so you can find length BT, Now you can use SOHCAHTOA again to find the length HT.

(edited 11 years ago)

Reply 2

TenOfThem

Original post by Tygra

This is an assignment question, so I do not want anyone to tell me the answer. I would just like some help and to be put in the right direction. I also need an explanation on what it means when it says "in terms of w

Thanks.

It means w or 3w or 5w/2 or w+7

I suggest that you draw out the right-angled triangles in 2D as a starting point

Reply 3

Tygra

Thanks guys.

I have just realised that triangle AHT IS a right angled triangle aswell. I thought the square representing the 90 degree angle was just for BHT.

So can you tell me if I am right with the first two questions? i) and ii)?

i) use triangle AHT to find HT in terms of w - would this be w x tan(45)?

ii)use trangle HTB to find BT in terms of w - would this be w x tan(45) / tan(30)?

Reply 4

TenOfThem

Original post by Tygra

Both incorrect unless I have misread

My error ... I was being particularly dim ... HT is w so I assumed you were wrong ... but of course I was not thinking about the value of tan(45)

(edited 11 years ago)

Reply 5

0x2a

Original post by Tygra

Both of your answers are correct.

Reply 6

Tygra

Thanks guys.

For question iii)use Pythagoros theorem in triangle ABT to write down the equation in w^2. Solve this equation, and thus find the height of the tree.

I know pythagoros theorem off by heart, but I've not had a question like this before. Would it be correct to have the equation wtan(45)/tan(30) = w^2 + 20^2?

Reply 7

0x2a

Original post by Tygra

Yup, that's correct.

Reply 8

TenOfThem

Original post by Tygra

Please stop including this

Do you know what tan(45) is

And the LHS needs to be squared as well

Which is handy since you should know what tan(30) is too

The answer is 12.

Even though kateislate gave me the answer which I didn't want I am having a hard time solving the equation for myself.

Do I start with (1/tan(30))^2 = w^2 + 20^2 ??

Reply 11

TenOfThem

Original post by Tygra

Even though kateislate gave me the answer which I didn't want I am having a hard time solving the equation for myself.

Do I start with (1/tan(30))^2 = w^2 + 20^2 ??

Apart from the 1 should be a w, yes

Reply 12

Tygra

This is how I did it, but I didn't get 12.

(w/tan(30))^2 = w^2 +20^2

w^2/ 1/3 = w^2 + 400

w^2 = 1/3(w^2 + 400)

w^2 = 1/3w^2 + 400/3

Multiply both sides by 3 to get

3w^2 = 1w^2 + 400

subtact 1w^2 from the RHS

2w^2 = 400

w^2 = 400/2

w = square root of 200 which = 14.1 to 1dp

Reply 13

TenOfThem

Original post by Tygra

This is how I did it, but I didn't get 12.

Why do you think 12 is the answer?

Reply 14

Tygra

That is what Kateislate posted. I assumed she is more advanced than me. Even though I'm an adult studying, this is only a higher GCSE question. She could be A level or even at degree level.

Is the answer not 12 TenOfThem??

Reply 15

TenOfThem

Original post by Tygra

Well, can you see an error with your working out?

Reply 16

TenOfThem

Original post by Tygra

That is what Kateislate posted. I assumed she is more advanced than me. Even though I'm an adult studying, this is only a higher GCSE question. She could be A level or even at degree level.

Looking at Kateislate's profile

She is in Y12 and has made 1 post on the Maths forum ... the one on this thread

Her A Levels are English, Media, and RS

She got a B in GCSE maths

(edited 11 years ago)

Reply 17

Indeterminate

Original post by TenOfThem

Looking at Kateislate's profile

She is in Y12 and has made 1 post on the Maths forum ... the one on this thread

Her A Levels are English, Media, and RS

She got a B in GCSE maths

lol, I think some people are always playing down the subject due to their lack of proficiency in it with stuff like "the answer is .... ".

Reply 18

Tygra

Original post by TenOfThem

Looking at Kateislate's profile

She is in Y12 and has made 1 post on the Maths forum ... the one on this thread

Her A Levels are English, Media, and RS

She got a B in GCSE maths

Oh right. Perhaps I should have looked at her profile.

No, I don't think I can see an error with my working out. I will take the answer I came up with.

Did you see the other question I posted TenOfThem on cumaltive frequency in my first post? Could you have a look at that for me please?

Reply 19

TenOfThem

Original post by Tygra

Oh right. Perhaps I should have looked at her profile.

No, I don't think I can see an error with my working out. I will take the answer I came up with.