Find x and y in a 30-60-90 right triangle with 60° opposite side 38

Question

Solve for x and y in a right triangle with one angle 60°, side opposite 60° length 38, right angle at the vertex between x and y.

Accepted Answer

x=38/√3=38√3/3, y=76√3/3

Answer

Step 1: Recognize this is a 30-60-90 special right triangle. The side 38 is opposite the 60° angle, which equals shortest leg × √3. Step 2: Calculate the shortest leg x: x = 38 / √3 = 38√3/3 (rationalize the denominator). Step 3: The hypotenuse y is twice the shortest leg, so y = 2 × 38√3/3 = 76√3/3.