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November 24th, 2014, 07:14 AM   #1
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Question 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?
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November 24th, 2014, 07:32 AM   #2
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$\displaystyle h = 7\sin(60)$

$\displaystyle A = \frac{1}{2} \cdot 7 \cdot 7\sin(60) = \frac{49\sqrt{3}}{4} \approx 21.22 \, cm^2$
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November 24th, 2014, 09:24 AM   #3
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I agree with you skeeter I do too
get it to somewhere around 21. But MY
facit say that it is 28
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November 24th, 2014, 10:40 AM   #4
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What says the "facit" is always correct?
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November 24th, 2014, 11:12 AM   #5
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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.
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November 24th, 2014, 12:20 PM   #6
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in this case, "they" are incorrect and a different method of calculation will not yield a different solution.
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November 24th, 2014, 12:48 PM   #7
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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.
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November 24th, 2014, 01:35 PM   #8
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Quote:
Originally Posted by DecoratorFawn82 View Post
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.
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November 24th, 2014, 01:45 PM   #9
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Quote:
Originally Posted by Timios View Post
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.
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November 24th, 2014, 09:44 PM   #10
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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
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