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November 24th, 2014, 07:14 AM  #1 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0  Calculate area of triangle when height undefined?
Hi! Need help calculating the height of a triangle that all sides is 7 cm in and 60 degrees in each angle I tried to calculate the height by doing: x/3,5 = tan 60 x = 6,1 (7*6,1)/2 = 21,35 cm² Area = (b * h)/2 Facit: 28 cm² What's wrong with this that I'm doing? 
November 24th, 2014, 07:32 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,886 Thanks: 1505 
$\displaystyle h = 7\sin(60)$ $\displaystyle A = \frac{1}{2} \cdot 7 \cdot 7\sin(60) = \frac{49\sqrt{3}}{4} \approx 21.22 \, cm^2$ 
November 24th, 2014, 09:24 AM  #3 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 
I agree with you skeeter I do too get it to somewhere around 21. But MY facit say that it is 28 
November 24th, 2014, 10:40 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,886 Thanks: 1505 
What says the "facit" is always correct?

November 24th, 2014, 11:12 AM  #5 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 
I didn't mean that the facit ALWAYS ARE CORRECT. But I thought that they had calculated it in another way so that it will be 28. But they may be wrong. 
November 24th, 2014, 12:20 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,886 Thanks: 1505 
in this case, "they" are incorrect and a different method of calculation will not yield a different solution.

November 24th, 2014, 12:48 PM  #7 
Senior Member Joined: Jan 2014 From: The backwoods of Northern Ontario Posts: 390 Thanks: 70 
Skeeter's answer is correct. Here is another way to calculate the area without using trig functions. Draw a height line segment from any vertex to the centre of the opposite side. Let the length of this segment be h. Then according to the Pythagorean Theorem: $\displaystyle 3.5^2 + h^2 = 7^2$ $\displaystyle h^2 = 7^2  3.5^2$ $\displaystyle h^2 = 49  12.25$ $\displaystyle h^2=36.75$ $\displaystyle h \approx 6.06218$ Area of one of the rightangled triangles is given by the formula ½bh. ∴ The area of both of them or the whole equilateral triangle is given by the formula bh. So the area of the equilateral triangle may be calculated as follows: $\displaystyle 3.5 \times 6.06218 \approx 21.22$ ∴ The area of the equilateral triangle is about $\displaystyle 21.22 cm^2$ By the way, what's a "facit"? Last edited by Timios; November 24th, 2014 at 12:59 PM. 
November 24th, 2014, 01:35 PM  #8  
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  Quote:
without long and unnecessary slippage, with the following formula $\displaystyle \mathcal{A}=\dfrac{l^2\sqrt3}{4}$ If we want to determine the height, we use the famous theorem Pitagoras. It will prove that : $\displaystyle h=\dfrac{l\sqrt3}{2}.$ Here, $\displaystyle l = 7$ is a particular situation.  
November 24th, 2014, 01:45 PM  #9 
Senior Member Joined: Apr 2014 From: Europa Posts: 575 Thanks: 176  "facit" may be some rolling from * Roman Empire. facit=make "Natura non facit saltus." "Barba non facit philosophum". Last edited by aurel5; November 24th, 2014 at 01:53 PM. 
November 24th, 2014, 09:44 PM  #10 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 
Sorry about saying "facit" I thought it was called the same in English as in Swedish. But what I mean a "facit" is: Facit = A paper where all answers are written (For mathbook exercises for example) Facit = Solution, answer 

Tags 
area, calculate, height, triangel, triangle, undefined 
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