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#1 2013-09-01 10:05:10

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

trig problems

1. What is the sine of an acute angle whose cosine is 7/25?

2. I'm standing at 300 feet from the base of a very tall building. The building is on a slight hill, so that when I look straight ahead, I am staring at the base of the building. When I look upward at an angle of 54 degrees, I am looking at the top of the building. To the nearest foot, how many feet tall is the building?

3. If A is an acute angle such that \tan A + \sec A = 2, then find \cos A.

4. In triangle GHI, we have GH = HI = 25 and GI = 30. What is \sin\angle GIH?

5. In triangle GHI, we have GH = HI = 25 and GI = 40. What is \sin\angle GHI? (Note: This is NOT the exact same as the previous problem!)


Genius is one percent inspiration and ninety-nine percent perspiration

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#2 2013-09-01 10:57:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#3 2013-09-01 10:59:17

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: trig problems

Hi

Last edited by anonimnystefy (2013-09-01 11:05:07)


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#4 2013-09-01 11:06:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

Online

#5 2013-09-01 11:15:15

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: trig problems

Hi bobbym

My bad! Thought it was GIH again. Your answer is correct for 5!


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#6 2013-09-01 11:18:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

All triangles should be named ABC by law. What if you have a bunch of them? No difference!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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#7 2013-09-01 11:19:07

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: trig problems

And, it would make even topologists happy. They already think all triangles are the same!


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#8 2013-09-01 11:20:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

Yea, they are weird.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

Online

#9 2013-09-01 11:36:40

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: trig problems

Definitely! And there's so many of 'em!


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#10 2013-09-01 11:41:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

I think we should consider all topologists the same.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

Online

#11 2013-09-01 14:26:51

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,016

Re: trig problems

Unfortunately, that does not reduce their numbers. Only one thing does.


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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#12 2013-09-01 15:14:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

Forcing them to computational math would reduce their numbers real quick.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

Online

#13 2013-09-02 05:48:22

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: trig problems

thanks


Genius is one percent inspiration and ninety-nine percent perspiration

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#14 2013-09-02 09:34:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 105,352

Re: trig problems

Hi;

Very good. Did you draw a diagram on that trig problem about the house?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

Online

#15 2016-03-14 12:19:03

numbergeek
Member
Registered: 2016-02-08
Posts: 4

Re: trig problems

mathstudent2000 wrote:

1. What is the sine of an acute angle whose cosine is 7/25?

4. In triangle GHI, we have GH = HI = 25 and GI = 30. What is \sin\angle GIH?

5. In triangle GHI, we have GH = HI = 25 and GI = 40. What is \sin\angle GHI? (Note: This is NOT the exact same as the previous problem!)

I'm working on these two problems. The triangle in question is not a right triangle. It's isosceles, but we can make some right triangles by adding the altitude from H to GI.

I can do number 4 -- my right triangle has sides KI= 15, HK= 20 and HI = 25. (I added K to be the foot of the altitude.)  So \sin\angleGIH=20/25=4/5.

But I'm stuck on  5 -- \angle GHI is not part of my right triangle. Half of it is \angle GIk. I thought I could say \sin\angle GHI= \sin\angle GHk + \sin\angle IHk = 20/25 +20/25 = 8/5. But that is not the answer you guys got.  Did you forget that GI is different in these two problems as well as the angle they are asking for? I'm really new to doing trig and not sure about my understanding  of how things work yet, so I can't tell if it is me doing something wrong, or if it is just a misreading of the problem, or what. Thanks.

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#16 2016-03-14 20:13:06

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,651

Re: trig problems

hi numbergeek

You cannot add sines together like that.  eg sin(90) = 1 but sin(180) is not 1 + 1.  It's because the sine graph is a curve.  And a sine can never be greater than 1.

So let's call J the midpoint of GI.

Then GJ = 20 and so sin(GHJ) = 20/25 and cos(GHJ) = 15/25

There is a formula for double angles:

Applying that here, we can say sin(GHI) = 2 x 20/25 x 15/25 = 96/100

Have a look here:

http://www.mathsisfun.com/algebra/trigo … index.html

Hope that helps.

Bob


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

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