Question

Find the length of side x to the nearest tenth. The angles /7 and x while the 30-60-90.

Answer 1

I’m missing the diagram or which side is 7 and which side is x. A 30–60–90 triangle always has side ratios

- short leg (opposite 30°) : long leg (opposite 60°) : hypotenuse = 1 : √3 : 2.

So if you tell me which of the three sides is 7 and which is x, you can get x from these formulas. Here are the three possible cases (values to nearest tenth):

- If the short leg = 7 (opposite 30°):
- long leg = 7√3 ≈ 12.1
- hypotenuse = 2·7 = 14

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

- If the hypotenuse = 7 (opposite 90°):
- short leg = 7/2 = 3.5
- long leg = (7/2)√3 ≈ 6.1

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