Question

Find the length of side x in simplest radical form with a rational denominator.
30°
60°
x
9
Answer
Attempt 1 out of 2

Answer 1

I’m missing which side the 9 is on in the diagram (short leg opposite 30°, long leg opposite 60°, or the hypotenuse). Which side is labeled 9?

Meanwhile, here are the possible answers for a 30°–60°–90° triangle (short leg = s, long leg = s√3, hypotenuse = 2s):

- If 9 is the hypotenuse: s = 9/2, long leg = (9√3)/2. So x = (9√3)/2 if x is the long leg, or x = 9/2 if x is the short leg.
- If 9 is the short leg (opposite 30°): s = 9, long leg = 9√3, hypotenuse = 18. So x = 9√3 if x is the long leg, or x = 18 if x is the hypotenuse.
- If 9 is the long leg (opposite 60°): s = 9/√3 = 3√3, hypotenuse = 6√3. So x = 3√3 if x is the short leg, or x = 6√3 if x is the hypotenuse.

Tell me which side in your picture is labeled 9 and which is x and I’ll give the single needed value.