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NonMathLover

Member

Registered: 2008-11-21

Posts: 7

Ack! Tangents? Cosines? Sines? What is this stuff?!

Hey you guys; I need some help on this hw problem...see, we're learning about tangents & cosines & stuff; but I am not grasping it *I was homeschooled last year, & I did ALGEBRA not this geometry, LOL!* so, I am trying to understand it easier.
Any help is appreciated.

Here's the problem:
It says 'Find the length of the missing side labeled x. Show your work.

Here's the pic of the problem, as I can't draw triangles on here very well:

Do you do a2+b2= C2?
or C2= a2+b2? Eh! & how do you convert the degrees or tell if it's a cosine, tangent or sine or not?
Thanks!

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That's me; I'm a non-math lover.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,424

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

The Sine rule would be useful here:

You know angle at R is 90° and the length of the side opposite it has to be found.
But then you also know angle r is 54° and the side opposite it is 4.5 cm.

Apply the formula, and you'd get the solution.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

The sine on calculator of 54 degrees, make sure calculator is in D, not R or G mode, if entering 54 degrees, D for degrees, R for Radians.
So either do COSine 36 degrees or do SINe 54 degrees, both are the
same thing.  Then set that result equal to (4.5 cm / x).

Last edited by John E. Franklin (2008-11-21 19:08:49)

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

Ganesh's formula is more usually used in triangles that don't have a right-angle.
It still works here, but you'd normally go with SOHCAHTOA.

This time, SOH is used because the two sides involved are the one Opposite your angle, and the Hypotenuse.

So sin 54 = Opposite/Hypotenuse = 4.5/x, which is what John said.

From there, rearrange and solve for x.

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Why did the vector cross the road?
It wanted to be normal.

NonMathLover

Member

Registered: 2008-11-21

Posts: 7

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

Okay, I'll try that. Thanks you guys!

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That's me; I'm a non-math lover.

NonMathLover

Member

Registered: 2008-11-21

Posts: 7

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

Sorry to double-post, but I think I am getting it more now.
However, how do I set it up? Do I do .8090/4.5? or 4.5/.8090? Eh!

Last edited by NonMathLover (2008-11-22 10:30:16)

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That's me; I'm a non-math lover.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

From above we had that sin 54 = 4.5/x.

Now multiply by x:
x sin 54 = 4.5

And divide by sin 54:
x = 4.5/sin 54 = 4.5/0.809... ≈ 5.6 cm

A useful thing to remember is that the hypotenuse (the side that doesn't touch the right-angle) is always the longest of the three sides.
If you'd got an answer that was less than 4.5, then you'd know that something had gone wrong.

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Why did the vector cross the road?
It wanted to be normal.

NonMathLover

Member

Registered: 2008-11-21

Posts: 7

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

Okay, thanks! That really helped.

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That's me; I'm a non-math lover.

Iv'egotit!Ithink

Member

Registered: 2009-05-18

Posts: 2

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

I'm having trouble understanding why I'm getting the wrong answer!
Can someone explain why?
Evaluate the six trigonometric functions of the angle x

The book says the answer is   sqrt5/5 , but don't understand why.

     |=
5   |   =     
     |--    =
     |_|____x_
         10

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Ack! Tangents? Cosines? Sines? What is this stuff?!

5√5 is the length of the hypotenuse of that triangle, because √(5² + 10²) = √(125) = 5√5.

That's not the answer, but it is required information to find the answer.

To find the 6 trigonometric functions of x, just use SOHCAHTOA to find sin, cos and tan.
(This is easy now that you know all three side lengths)

Then divide 1 by each of those to get cosec, sec and cot respectively.

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Why did the vector cross the road?
It wanted to be normal.