In a 30-60-90 triangle, where the long leg is 12, what is the length of the short leg?

Question

In a 30-60-90 triangle, where the long leg is 12, what is the length of the short leg?

1 Answer

Impact of this question

17743 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-15T19:10:50

The length of short leg $= 6.928$ $=6.928$

Explanation:

$30^{o}$ $30^o$ - $60^{o}$ $60^o$ - $90^{o}$ $90^o$ is a special kind of right-triangle in which sides exist in ratio $S L : L L : H = 1 : \sqrt{3} : 2$ $SL:LL:H = 1:sqrt(3):2$

where
$S L =$ $SL=$ Short Leg,
$L L =$ $LL=$ Long Leg,
$H =$ $H=$ Hypotenuse

The side-lengths can also be calculated with these relations
$S L = \frac{1}{2} H$ $SL=1/2H$ or $S L = \frac{1}{\sqrt{3}} L L$ $SL=1/sqrt3LL$
$L L = \frac{\sqrt{3}}{2} H$ $LL=sqrt3/2H$ or $L L = S L \sqrt{3}$ $LL=SLsqrt3$

Therefore, if $L L = 12$ $LL=12$

$S L = \frac{1}{\sqrt{3}} \times 12 = 4 \sqrt{3} = 6.928$ $SL=1/sqrt3xx12=4sqrt3=6.928$

Science

Math

Humanities

... and beyond

In a 30-60-90 triangle, where the long leg is 12, what is the length of the short leg?

1 Answer

Explanation:

Related questions

Impact of this question