Answer:
y = 9 units
x = 9√3 units
Explanation:
We know that this is a 30-60-90 triangle since the sum of the interior angles in a triangle is 180 and 180 - (90 + 30) = 60.
In a 30-60-90 triangle, the measures of the sides are related by the following ratios:
- We can call the side opposite the 30° angle "s" and its the shorter leg.
- The side opposite the 60° angle is √3 times the length of the shorter leg and its the longer leg. So it's s√3
- The hypotenuse (side always opposite the 90° or right angle) is twice the length of the shorter side. So it's 2s.
Step 1: Since the hypotenuse is 18 units, we can find y by dividing 18 by 2:
y = 18/2
y = 9
Thus, the length of y is 9 units
Step 2: Since we now know that the length of the side opposite the 30° angle by √3 to find x:
x = 9√3
9√3 is already simplified so x = 9√3