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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: 2,947 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 right-angled 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
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Quote:
 Originally Posted by DecoratorFawn82 Hi! Need help calculating the height of a triangle that all sides is 7 cm in and 60 degrees in each angle
Equilateral triangle area can be calculated,

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
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Quote:
 Originally Posted by Timios By the way, what's a "facit"?

"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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mathsheadache Algebra 5 October 20th, 2014 07:38 PM caters Algebra 31 March 31st, 2014 01:09 PM clankill3r Algebra 5 January 2nd, 2012 08:34 AM Valar30 Calculus 1 April 22nd, 2011 11:43 AM hahaha Algebra 7 November 12th, 2007 09:38 AM

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