Question

or

Find a.
a
3
2 mm
45°
45°
Write your answer in simplest radical form.

Answer 1

I’m missing the diagram, so I’m not sure which side is labeled 3 (or whether it was "3/2 mm"). For a 45°–45°–90° triangle the sides follow the ratios
leg : leg : hypotenuse = 1 : 1 : √2.

Here are the likely cases:

- If the given side 3 is a leg, then the hypotenuse a = 3·√2 = 3√2.
- If the given side is 3/2 mm (i.e. 1.5 mm) and that is a leg, then a = (3/2)·√2 = (3√2)/2 mm.
- If the given side 3 is the hypotenuse, then each leg a = 3/√2 = (3√2)/2.

Tell me which side is labeled 3 (or upload the diagram) and I’ll confirm the final answer.