My Math Forum Calculate area of triangle when height undefined?

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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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Joined: Apr 2014
From: Europa

Posts: 584
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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
Senior Member

Joined: Apr 2014
From: Europa

Posts: 584
Thanks: 177

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

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