Given 30-60-90 triangle with sides p\sqrt(6) , p\sqrt(2 ), q\sqrt(3); find p, q

What side is \(\frac{p}{\sqrt2}\)? What side is \(\frac{p}{\sqrt6}?\)

We are given a 30-60-90 triangle ABC with sides p6​, p2​, and q3​. We are asked to find the values of p and q. We can start by using the fact that the sides of a 30-60-90 triangle are in the ratio 1:3​:2. This means that we can write the following equations:

p2​p6​​=3​q3​p2​​=1

Simplifying these equations, we get:

2​6​​=3​3​2​​=q1​

Solving the first equation, we find that 6​=6​. This is true, so our first equation is valid.

Solving the second equation, we find that q=6​.

Therefore, the values of p and q are p = 1/sqrt(3) and q = sqrt(6)