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


2 times

3 times

√2 times

√3 times

2 Answers
Feb 9, 2018

See below

Explanation:

#sqrt3# times

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

Feb 9, 2018

#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:

dummies.com

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

enter image source here