Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Help me with this triangle!

I have a triangle HPN with two side lengths HP = 54km and HN = 75km and included angle 15 degrees. Let the angles opposite HP and HN be

and

  respectively. By use of the cosine rule I get

Next, I use the sine rule to solve for remaining angles:

The last angle I will find using the sine rule again.

Ok cool, this triangle has 92.915 degrees, I think I'm going mad...

Last edited by Identity (2007-08-22 02:05:07)

reddog

Member

Registered: 2007-07-23

Posts: 7

Re: Help me with this triangle!

See this http://www.mathhelpforum.com/math-help/trigonometry/17959-odd-triangle.html

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help me with this triangle!

Your 46.456 degrees must be subtracted from 180 degrees to get the obtuse angle where the sine or height in the 2nd quadrant is the same height as the 46.456 angle.
Also your #'s are just slightly off because you are rounding, but that's just a tiny problem.
The angles I get are 133.536753 degrees for angle P.
And 31.463247 degrees for angle N.
And the given 15 degrees for angle H.
Also side NP is 26.7768707 km

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Help me with this triangle!

It is important to draw the triangle as accurately as you can with a proper 15 degree angle that
is between 7 and 25 degrees. You can do this by studying a protractor, or
by dividing a right angle in half for 45, and in thirds after that for 15.
You should also subtract 54 from 75 and know that NP will be bigger than that 21 due to the 15 degree spread, instead of near zero degrees.
If an angle in the triangle is very close to 90 degrees, and you don't know if it is 89 or 91 degrees, which have the same sine result, then you can compare the 3 sides with pythagoreans theorm, and decide if the sort-of hypotenuse is too big or too small.    c^2 > a^2 + b^2, for 91 degrees.
c^2 < a^2 + b^2, for 89 degrees.   That's what I think.
Sorry I haven't explained graphically with pictures.

So if you get 89 degrees, then see how far you are from 90 and add that to 90 to get 91.
Or you can subtract 89 from 180, like I mentioned in the last post subtracting the 46.46 from 180.
But you can subtract it from 90 and then add it to 90.  90-46 is 44 and 90+44 is 134.  See?

Last edited by John E. Franklin (2007-08-23 12:39:27)

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igloo myrtilles fourmis

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Help me with this triangle!

Thanks reddog and John!