Question

What is the length of NM?

Answer 1

See below :)

Explanation:

We know that these traingles are all similar. We can see the angle NMK is 60 degrees so we also know that JNK is 60 degrees. Now we know that all of the triangles are 30-60-90 triangles. JN is 3, so from the "leg opposite to 30 degree theorem", we know that NK is two times JN which is 6. Then from the same theorem, we know that NM is NK divided by the square root of 3

`(6)/(\sqrt3)`

We can't have fractions that have irrational numbers in the denominator of a fraction so we multiply it by root3 over root3

`(6)/(\sqrt3)` *
`(\sqrt3)/(\sqrt3)`

This then makes it 6 times root 3 over 3

`(6\sqrt3)/(3)`

We then get
`2√(3)`