# How do you find the remaining side of a #30^circ-60^circ-90^circ# triangle if the side opposite #60^circ# is 6?

##### 2 Answers

Use Trigonometric identities.

#### Explanation:

Let us assume the side next to

Then use the Pythagorean theorem.

We know:

Then:

The side lengths are:

#### Explanation:

The sides of a

In math:

#"side opposite 60°"/"side opposite 30°"=sqrt3/1=sqrt3#

#"side opposite 90°"/"side opposite 30°"=2/1=2#

We are given the side opposite 60° to be length 6. So, given that the ratio of "the 60° side"-to-"the 30° side" is

#"side opp. 60°"/"side opp. 30°"=sqrt3#

#6/"side opp. 30°"=sqrt3#

#" "6/sqrt3" "="side opp. 30°"#

#" "(6sqrt3)/3" "="side opp. 30°"#

#" "2sqrt3" "="side opp. 30°"#

And, since "the 90° side" is 2 times as long as "the 30° side", we have

#"side opp. 90°" = 2xx "side opp. 30°"#

#"side opp. 90°" = 2xx 2sqrt 3#

#"side opp. 90°" = 4sqrt 3# .