A/Sin45=b/Sin60=c/Sin75
find
a:b:c

4 : 2√6 : √3 + 1

Step-by-step explanation:

Our equation is:

These are a few trig identities that we want to memorize:

- sin(45) = √2/2

- sin(60) = √3/2

- sin(75) = sin(45 + 30) = sin(45) * cos(30) + sin(30) * cos(45) = (√2/2)(√3/2) + (1/2)(√2/2) = √6/4 + √2/4 = (√6 + √2)/4

Put these in:

Then the ratio of a:b:c is:

(6√2 - 2√6) : (6√3 - 6) : (2√6), which simplifies to:

4 : 2√6 : √3 + 1

If you wanted, you could use a calculator to find the decimal form of that.

that is the solution to the question