In a 30-60-90 triangle, what is the length of the long leg and hypotenuse if the short leg is 5 in long?

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In a 30-60-90 triangle, what is the length of the long leg and hypotenuse if the short leg is 5 in long?

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Answer 1 · 2015-11-15T19:04:09

$L = 10, h = 5 \sqrt{3}$ $L = 10, h = 5 sqrt 3$

Explanation:

You have half an equilateral triangle of sides $(L; \frac{L}{2}; h = L \frac{\sqrt{3}}{2})$ $(L ; L/2 ; h = L sqrt 3/2)$

L is the hypotenuse, $\frac{L}{2} = 5$ $L/2 = 5$ is the short one, h is the long one.

Answer 2 · 2015-11-15T19:40:36

Length of long leg $= 3.464$ $=3.464$ in, Length of hypotenuse $= 10$ $=10$ in

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 $S L = 5$ $SL=5$ in

$L L = 2 \sqrt{3} = 3.464$ $LL=2sqrt3=3.464$ in
and
$H = S L \times 2 = 5 \times 2 = 10$ $H=SLxx2=5xx2=10$ in

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In a 30-60-90 triangle, what is the length of the long leg and hypotenuse if the short leg is 5 in long?

2 Answers

Explanation:

Explanation:

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