In 30-60-90 triangle, where the length of the long leg is 9, what is the length of the hypotenuse and the short leg?

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In 30-60-90 triangle, where the length of the long leg is 9, what is the length of the hypotenuse and the short leg?

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Answer 1 · 2018-03-27T17:08:20

Since it's a 30-60-90 triangle, the hypotenuse should be $6sqrt(3)$ and the short leg is $3sqrt(3)$

Explanation:

In a 30-60-90 triangle, the sides can be described as such:

Short side: $1$
Hypotenuse: $2$
Long Side: $sqrt(3)$

These can be considered ratios. If you look at it in terms of sine and cosine, this becomes a bit clearer, since sine and cosine gives you the ratio of the sides:

$cos(60)="short"/"hyp"=1/2 rArr "short"=1, "hyp"=2$

$sin(60)="long"/"hyp"=sqrt(3)/2 rArr "long"=sqrt(3), "hyp"=2$

$tan(60)="long"/"short"=sqrt(3) rArr "long"=sqrt(3), "short"=1$

since we know the ratios, we can multiply them by a constant, $x$

$"short"=1x=x$

$"hyp"=2x$

$"long"=sqrt(3)x=9$

Now that we have an equation which describes the length of the long leg in terms of the side ratios, we can solve for $x$ , and quickly solve for the short side and hypotenuse:

$sqrt(3)x=9 rArr x=9/sqrt(3)=3*sqrt(3)^2/sqrt(3)$

$color(red)(x=3sqrt(3))$

$color(blue)("short"=x=3sqrt(3))$

$color(green)("hyp"=2x=6sqrt(3))$

Answer 2 · 2018-03-27T17:22:05

Use trigonometric function

Explanation:

$b=9$
$alpha=30°$
$beta=60°$
$gamma=90°$
my pic
$a=?$
$c=?$
$tan(30°)=a/b$
$a=tan(30°)b=3*√3$
$cos(30°)=b/c$
$c=b/cos(30°)=6*√3$

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In 30-60-90 triangle, where the length of the long leg is 9, what is the length of the hypotenuse and the short leg?

2 Answers

Explanation:

Explanation:

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