Math Is Fun Forum

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Trigonometry

Hi brothers and sisters (we're a family right?)

I can't thank you enough for your kind assistance since I joined the family. It's good to know there's always someone out there to solve our problems.

At the moment we're learning trig in Core Math and today the teacher brought a few questions on elevation and depression stuff for us to work out. There were three in all. I was able to solve the first, someone did the second. And the third? All 45 students struggled with that with different solutions coming in. The period ended with no one solving so the teacher promises to include it in a quiz on Thursday. I need help solving it before then. [Thursday is only two days away].

The feet of two vertical poles of height 3m and 7m are in line with a point P on the ground, the shorter pole being between the taller pole and P, and at a distance of 20m from P. The angle of elevation of the top (T) of taller pole from the top (R) of smaller pole is 30°. Calculate the
           (a) distance RT
           (b) distance of the foot of the taller pole P, correct to 3 s f
           (c) angle of elevation of T from P correct to 1 dp

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Only a friend tells you your face is dirty.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Trigonometry

What will the diagram be like when we've interpreted the above information?

Dear bobbym, I haven't worked this myself and I don't know what is the right answer. Thanks for helping out anyway. Could you please give me a systematic approach to your solution?

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Only a friend tells you your face is dirty.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Trigonometry

Time was against me so I couldn't type this second one (also to appear in the test).

From a horizontal distance 8.5 km, a pilot observes that the angles of depression of the top and base of a control tower are 30° and 33° respectively. Calculate, correct to 3 s f
(i) the distance between the pilot and base of the control tower
(ii) the height of the control tower.

Thanks as always.

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Only a friend tells you your face is dirty.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry

Hi;

This is how I would draw it.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Trigonometry

Thanks bobbym. Looking at the question and the diagram here, DP is 20m?

Please why doesn't the hypotenuse extend to the point P?

Also with the diagram, how do we arrive at your answer for (a)?

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Only a friend tells you your face is dirty.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry

Please why doesn't the hypotenuse extend to the point P?

The feet of two vertical poles of height 3m and 7m are in line with a point P on the ground,

It seems to say that the feet (bases) of the poles line up with P, it does not say anything about the tops of the poles. But I would suggest that you get a clarification if you can.

Also with the diagram, how do we arrive at your answer for (a)?

One way would use SOHCAHTOA.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Trigonometry

Hi;

For the problem in post #1 I'd probably use this as my starting drawing, before going on to do any workings:

Just some small differences from Bobby's in post #5.

Last edited by phrontister (2017-02-27 00:36:18)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Trigonometry

hi math9maniac

Here's a diagram for the post 4 question:

There are the two angles at P (bit crowded on my diagram to show both clearly.)

So you can use opp = adj x tan(angle) for the top and bottom of the tower and subtract to get the height of the tower.

Phro:  I thought for a moment that your diagram was for this one.  I known you're upside down, but having the pilot lower than the tower ??? Then I realised it wasn't for that problem. 

Question 1:

TE must be 4.

So trig will get TR and ER (=BD)

Then calculate BP and use trig again on triangle TBP to get angle TPB

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Trigonometry

Hi Bob;

Phro:  I thought for a moment that your diagram was for this one.  I known you're upside down, but having the pilot lower than the tower ??? Then I realised it wasn't for that problem. 

You probably hadn't seen my edit to post #8 from a few minutes ago (my time) before you wrote that. I'd've thought the time difference thingie would've kicked in in time....

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Trigonometry

hi Phro,

No.  It was just a joke about pilots flying up-side-down.  Don't worry.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,884

Re: Trigonometry

Thanks, Bob...I'll try not to worry. My comment was a joke about your joke, but please don't let that worry you.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Trigonometry

No worries.

B

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Trigonometry

Also with the diagram, how do we arrive at your answer for (a)?

One way would use SOHCAHTOA.

Alright. So what are the dimensions of the adjacent and opposite sides to give a hypotenuse of 8 as you solved?

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Only a friend tells you your face is dirty.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Trigonometry

Thanks Bob, Phro and bobbym for your assistance. I'll give you feedback on how the test goes tomorrow.

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Only a friend tells you your face is dirty.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Trigonometry

So what are the dimensions of the adjacent and opposite sides to give a hypotenuse of 8 as you solved?

TE = 4 and the angle opposite is 30.  We want the hypotenuse TR.

TE/TR = sin(30) =>  TR = TE / sin(30) = 4/0.5 = 8

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry

Hi;

You know that ET is equal to 4 and angle TRE is 30 degrees. So:

SOHCAHTOA is an acronym for all these angle and side problems of a right triangle.

SOH means Sine = Opposite / Hypotenuse.

Can you finish?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

math9maniac

Member

From: Tema

Registered: 2015-03-30

Posts: 443

Re: Trigonometry

Yes bobbym. I'll finish it. Thanks.

Thanks Bob for explanation.

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Only a friend tells you your face is dirty.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Trigonometry

Hi;

Please post your work so that we can see it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.