Question

Find the length of side xx to the nearest tenth.
30°
60°
x
7

Answer 1

I’m missing the diagram — I need to know which side the 7 corresponds to (opposite 30°, opposite 60°, or the hypotenuse). For a 30°–60°–90° right triangle the side ratios are short:long:hypotenuse = 1:√3:2, so the possible values for x (rounded to the nearest tenth) are:

- If 7 is the hypotenuse:
- short (opposite 30°) = 7/2 = 3.5
- long (opposite 60°) = (7/2)·√3 ≈ 6.1

- If 7 is the short leg (opposite 30°):
- long (opposite 60°) = 7·√3 ≈ 12.1
- hypotenuse = 2·7 = 14.0

- If 7 is the long leg (opposite 60°):
- short (opposite 30°) = 7/√3 ≈ 4.0
- hypotenuse = 2·(7/√3) ≈ 8.1

Tell me which side in the diagram is the 7 (or upload the picture) and I’ll give the exact x.