One side of the equilateral triangle is 12cm .find its area

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

8 0

Triangle area formula 1/2bxh
12/2=6 6x12=72

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Given that θ terminates in Quadrant III and tanθ 5/12= , find cscθ

Komok [63]

$\bf tan(\theta)=\cfrac{opposite}{adjacent}
\qquad \qquad 
csc(\theta)=\cfrac{hypotenuse}{opposite}
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tan(\theta)=\cfrac{5}{12}\cfrac{\leftarrow opposite=b}{\leftarrow adjacent=a}\\\\
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\textit{let's use the pythagorean theorem to get the hypotenuse "c"}
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c^2=a^2+b^2\implies c=\pm\sqrt{a^2+b^2}\implies c=\pm\sqrt{12^2+5^2}
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\boxed{c=\pm 13}$

now, the square root gives us the +/- version, so.. which is it? well, the hypotenuse is just a radius unit, is never negative, just the radius unit, so just the absolute value of that or the version 13, so c = 13

now, that we know what the hypotenuse "c" is, well

$\bf csc(\theta)=\cfrac{hypotenuse}{opposite}\implies csc(\theta)\cfrac{13}{5}$