Question

or

Find n.
n
8 yd
30°
60°
Write your answer in simplest radical form.

Answer 1

I don't have the diagram, so I can't tell which side is labeled n. For a 30°–60°–90° triangle the side ratios are short:long:hypotenuse = 1:√3:2. Here are the possible answers depending on which side is 8 yd:

- If 8 yd is the hypotenuse: short = 8/2 = 4 yd, long = 4√3 yd. So n = 4 (if n is opposite 30°) or n = 4√3 (if n is opposite 60°).

- If 8 yd is the short leg (opposite 30°): hypotenuse = 2·8 = 16 yd, long = 8√3 yd. So n = 16 or n = 8√3 as appropriate.

- If 8 yd is the long leg (opposite 60°): short = 8/√3 = (8√3)/3 yd (rationalized), hypotenuse = 2·(8/√3) = (16√3)/3 yd. So n = (8√3)/3 or n = (16√3)/3 as appropriate.

Tell me which side in the picture is labeled n (or send the diagram) and I’ll give the single correct value.