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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

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.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

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.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

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.**

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

thanks

Genius is one percent inspiration and ninety-nine percent perspiration

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,201

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.**

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

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,566

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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