
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 2,947 Thanks: 1555 
$\displaystyle h = 7\sin(60)$ $\displaystyle A = \frac{1}{2} \cdot 7 \cdot 7\sin(60) = \frac{49\sqrt{3}}{4} \approx 21.22 \, cm^2$ 
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: 2,947 Thanks: 1555 
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: 2,947 Thanks: 1555 
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: 584 Thanks: 177  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: 584 Thanks: 177  "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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculate the radius of the cylinder if its height is 2.80m?  mathsheadache  Algebra  5  October 20th, 2014 07:38 PM 
Height unknown but need area.  caters  Algebra  31  March 31st, 2014 01:09 PM 
calculate width and height  clankill3r  Algebra  5  January 2nd, 2012 08:34 AM 
Change of triangle height  Valar30  Calculus  1  April 22nd, 2011 11:43 AM 
reduce area, calculate new height,width  hahaha  Algebra  7  November 12th, 2007 09:38 AM 