Question

in the figure, triangle BDE has the following angle measure:angle B=40 degrees angle D=60 degress and angle E=80

Answer 1

I don't see the figure, but from what you wrote the triangle BDE has angles B = 40°, D = 60°, E = 80°. A few immediate facts and useful formulas:

- Check: 40° + 60° + 80° = 180°, so the angles are consistent.
- Classification: all angles < 90°, so triangle BDE is acute and (since all angles different) scalene.
- Ordering of side lengths (by opposite angles):
- side BD is opposite angle E = 80° → BD is the longest,
- side BE is opposite angle D = 60° → intermediate,
- side DE is opposite angle B = 40° → shortest.

- Law of sines (useful to find side ratios or absolute lengths if one side is given):
BD / sin 80° = BE / sin 60° = DE / sin 40° = 2R (circumdiameter).
So the side ratios are BD : BE : DE = sin 80° : sin 60° : sin 40°
≈ 0.9848 : 0.8660 : 0.6428 ≈ 1.532 : 1.347 : 1.

- Area: if you know one side, say DE = a, then the area = (1/2)·(a)·(other side)·sin(included angle) or use
Area = (1/2)·(DE)·(BE)·sin ∠D (i.e. sin 60°) once you have BE from the law of sines.

If you want a specific numeric side length, area, circumradius, inradius, or something else, tell me which side (or another measurement) from the figure is known and I’ll compute the rest.