Question

Find the length of side xx to the nearest tenth.
30°
60°
x
√6

Answer 1

I don't have the diagram — can you confirm which side is labeled √6 and which is x (is √6 the hypotenuse, the short leg opposite 30°, or the long leg opposite 60°)?

Meanwhile here are the possible answers (30°–60°–90° triangle ratios: short:long:hyp = 1:√3:2), rounded to the nearest tenth:

- If √6 is the hypotenuse:
- x = short leg (opposite 30°) = (1/2)√6 ≈ 1.2
- x = long leg (opposite 60°) = (√3/2)√6 ≈ 2.1

- If √6 is the short leg (opposite 30°):
- x = hypotenuse = 2√6 ≈ 4.9
- x = long leg = √3·√6 = √18 ≈ 4.2

- If √6 is the long leg (opposite 60°):
- x = short leg = √6/√3 = √2 ≈ 1.4
- x = hypotenuse = (2/√3)√6 = 2√2 ≈ 2.8

Tell me which labeling matches your diagram and I’ll give the single correct value.