Answer:
y = 6√3 and x = 6
Step-by-step explanation:
this is a 30-60-90 triangle. The side opposite the 30° angle corresponds to the side of length 1 in the most basic 30-60-90 triangle; the side opp. 60° to the side of length √3; and the hyp. to the side of length 2.
To find y, write and solve an equation of ratios, as follows:
adj side adj side (adjacent to the 30° angle)
y √3
hypo hypo then (cross multiplying): 2y = 12√3, and
12 2 y = 6√3
If the hypo here is 12 and the adj side (y) is 6√3, then we can use the Pyth. Theorem to find the third side (x):
[12]² = [6√3]² - x² ↔ 144 = 36(3) - x² ↔ 36 = x². So x = 6 here.
