Question

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

2 times

3 times

√2 times

√3 times

Answer 1

See below

Explanation:

`sqrt3` times

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

Answer 2

`sqrt 3` times.

Explanation:

In a `30^@"-"60^@"-"90^@` triangle, the `60^@` angle opens to the long leg, so

`tan 60^@="opposite"/"adjacent"="long leg"/"short leg"`

We also know that `tan60^@=sqrt3`, so we get

`tan60^@ = "long leg"/"short leg"`

`=>sqrt3" "="long leg"/"short leg"`

`=>"long leg" = sqrt3 xx "short leg"`

A common diagram for such a triangle is:

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