In a 30-60-90 triangle, the long leg is _____ the short leg?

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In a 30-60-90 triangle, the long leg is _____ the short leg?

2 times

3 times

√2 times

√3 times

2 Answers

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Answer 1 · 2018-02-09T01:25:59

See below

Explanation:

$\sqrt{3}$ $sqrt3$ times

Please see the link below for the more details:
https://www.freemathhelp.com/triangle-30-60-90.html

Answer 2 · 2018-02-09T01:32:42

$\sqrt{3}$ $sqrt 3$ times.

Explanation:

In a $30^{\circ} - 60^{\circ} - 90^{\circ}$ $30^@"-"60^@"-"90^@$ triangle, the $60^{\circ}$ $60^@$ angle opens to the long leg, so

${tan 60}^{\circ} = \frac{opposite}{adjacent} = \frac{long leg}{short leg}$ $tan 60^@="opposite"/"adjacent"="long leg"/"short leg"$

We also know that ${tan 60}^{\circ} = \sqrt{3}$ $tan60^@=sqrt3$ , so we get

${tan 60}^{\circ} = \frac{long leg}{short leg}$ $tan60^@ = "long leg"/"short leg"$

$\Rightarrow \sqrt{3} = \frac{long leg}{short leg}$ $=>sqrt3" "="long leg"/"short leg"$

$\Rightarrow long leg = \sqrt{3} \times short leg$ $=>"long leg" = sqrt3 xx "short leg"$

A common diagram for such a triangle is:

![dummies.com]( useruploads.socratic.org )

This and the one for the 45-45-90 triangle are useful to memorize!

enter image source here

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In a 30-60-90 triangle, the long leg is _____ the short leg?

2 times

3 times

√2 times

√3 times

2 Answers

Explanation:

Explanation:

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