Nov Math II Law of Cosine Quesiton

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1

<p>Guys you know that question which said there was an isosceles triangle with sides 5,10,10 and asked you to calculate the largest angle?</p>

<p>For that most people con CC say the answer was 29 something...but im fairly confident im right...</p>

<p>c^2 = a^2 + b^2 - 2abcosine(C)</p>

<p>5^2 = 10^2 + 10^2 - 2(10)(10)cosine(c)
25 - 200 = -2(100)cos(c)
-175/-200 = cos(c)
cos(c) = .875
Do inverse cos(.875) you get = 28.955 deg. which is...the SMALLEST angle. so
180 - 28.955 = 151.044
since its isosceles, divide this angle by 2 to get the largest angle
151.0444/2 = 75.522 degress. Which was an answer i belive. thats what i put. im pretty sure this is right.</p>

<p>and if the answer was ~29 or w/e it would have to be the largest angle, therefore since it is isoseceles 29 x 2 = 58 [[sum of two angles is 58]] 180 - 58 = 122. clearly a larger angle. so how can ~29 deg. be right?</p>

2

<p>It wasnt asking for the largest angle.It was asking for the angle between both congruent legs of the isosceles triangle.</p>

3

<p>yeah it asked which was the angle between the congruent sides</p>

4

<p>It never asked for the largest angle. It asked for the angle created by the two equal sides.</p>

5

<p>Fourthed … (what the other 3 people said)</p>

6

<p>fifth-ed…</p>

7

<p>[TRIANGLE</a> CALCULATOR Solves 4 Cases of Triangles - SSS - SAS - ASA - AAA](<a href=“http://www.1728.com/trig4.htm]TRIANGLE”>TRIANGLE CALCULATOR Solves 4 Cases of Triangles - SSS - SAS - ASA - AAA)</p>

<p>Sides; 10, 10, 5
Angles; 75.522, 75.522, 28.955</p>

8

<p>so the answer of this question is 29 right?</p>

9

<p>the answer is 29, yep. 100%</p>

10

<p>why used law of cosines and complicated trigs -_-. Just divide the base into 2. (5/2). Then take cos-1(2.5/10). the angle should be 75.5. Double that, then 180-the result, it should give you the answer without wasting much of your time D:</p>

11

<p>or you could use law of cosines by doing most of it in your head then punching a few numbers in on the calculator. =]. cos^-1(-175/-200)=28.955</p>

12

<p>or, logically, Isosceles Triangle; Two Equal Angles > Smallest Angle; Meaning; TEA > 60 degrees each; or Smallest < 60 degrees, which only 29 fit. 180/3 = 60; ~ 75;75;30.</p>

13

<p>draw a line from the 30 degree down to the side of 5</p>

<p>it splits the triangle into 2 right triangles.
Solved.</p>

14

<p>using law of cosines is way faster than thinking a whole bunch of stuff, that’s what calculators are great for:))</p>

15

<p>crappp</p>

<p>I think I put 75 in my rush…</p>

16

<p>GUYS we didn’t have to do ANY math at all.</p>

<p>Just realize that only ONE of the choices was below 60.</p>

<p>Just pick that (29) and you’ve got the question answered in 5 seconds. :slight_smile: This was a critical reason why I had extra time on the last 5 questions.</p>

17

<p>So the answer was 29, right? If so,…
then Yay! Now I know I got at least one question right on that test!</p>

18

<p>I understand why 29 was right, but I don’t understand how you know it is right just because it is less than 60. Can someone explain this to me?</p>

19

<p>If there are 2 sides of the same length (aka isosceles) and the third is SMALLER than the two, then the angle for that third side is smaller than the other two. An equilateral triangle is 60-60-60. If 1 angle is smaller than the other two (which will be the same since they are across of same sides) then it has to be less than 60 degrees. No other way is possible, unless you change the very definition of what constitutes a triangle.</p>

20

<p>Ah, yes. Can’t believe I didn’t see that. Thanks, DMOC.</p>