Answer:
D
Step-by-step explanation:q
If you have a 30 degree reference angle, the side opposite (the side not part of the reference angle) is 1/2 the size of the hypotenuse.
Since the side opposite is 12, the hypotenuse is easily found.
1/2 = opposite / hypotenuse
1/2 = 12 / hypotenuse Cross multiply
hypotenuse = 2 * 12
hypotenuse = 24
Now use the Pythagorean Theorem to get the third side.
c = 24
a = 12
b = ?
a^2 + b^2 = c^2
12^2 + b^2 = 24^2
144 + b^2 = 576 Subtract 144 from both sides.
b^2 = 576 - 144
b^2 = 432
Now you have to factor 432 down to its primes
432 = 2 * 2 * 2 * 2 * 3 * 3 * 3
The rule is for every two 2s you take one outside the root sign and throw the other one away. If there are an odd number of factors, leave one of them under the root sign.
sqrt(b^2) = sqrt(432)
b = 4 * 3sqrt(sqrt(3))
b = 12 sqrt(3)
Answer
r = 12*sqrt(3)
t = 24
The answer is D