Question

Select all the correct answers.

Which three pairs of side lengths are possible measurements for the triangle?
30°
H
60°
OGH=2√3, HI = 2
GH=2, HI= 2√3
GH = 8√2, GI = 16
GH=8, GI=16
GH= 8√3, GI=16
HI=7, GI=14

Answer 1

GH = 2
`√(3)`, HI = 2

Explanation:

30-60-90 triangles are cool because their sides are in the ratio 1,
`√(3)`, 2 so you should try to remember them because they come in handy in real life sometimes.

I've attached a picture of one that will help explain the next bit.

• The shortest side is designated as 1 unit long.
• The next longest side (the other side of the right angle) is that length times
  `√(3)` (which is 1.732 btw, and you should probably start remembering that, along with pi and
  `√(2)`).
• And the hypotenuse, which of course is the longest side, is 2 units long, or twice the shortest leg.

See that on the drawing?

Okay, so your problem is asking about the two short sides isn't it? Not the hypotenuse.

So we know that we're looking for a number for the short side, then that same number multiplied by
`√(3)` for the other side.

Do you see the answer already? It's the one of the form (a, a
`√(3)`).

So of course it's the first choice: 2
`√(3)`, 2