Answer:
a = 12
b = 6
Explanation:
You have a 30°-60°-90° triangle which is a special right triangle. We memorize the ratios of the sides and can find the sides given just one side, by using the relationships between the sides, so we don't have to use trig ratios.
Generally, the LONGEST side (hypotenuse) is twice the shortest side. Or, the SHORTEST side is half the longest side (hypotenuse). The LONGER LEG is the short leg × sqrt(3).
Or the SHORT LEG is the
longer leg/sqroot(3)
You are given the long leg here. You have:
Long leg = 6sqroot(3)
So the short leg must be 6.
bc, longer leg IS Short leg×sqroot(3)
short leg =6
Then the LONGEST side (hypotenuse) has to be twice that.
LONGEST side = 12
Where it says "Prove side c" maybe that is like doing a check.
6^2 + (6sqrt3)^2 = 12^2
36 + 108 = 144
144=144
CHECK!