Geometry, one problem

[wooden wave]

AB is perpendiclar.
Angles ABC and ABD are both 90.
Triangles ABC and ABD are congruent by SAS criterion (AB common, right angle, BC = BD given)
Thus AC and AD are equal (congruent triangles)
Angles opposite to equal sides are equal (see triangle ACD)
AC = AD so Angle ACD is 60 too.
So ange CAD is 60 too (angles in triangle ACD sum to 180)
So all sides of triangle ACD are equal to 8.
AC is 8.
Using trigonometry in right angled triangle ABC: AB is 4.

[final grotto]

thank you so much! just tell me please what SAS criterion means?

[wooden wave]

If in 2 triangles a corresponding side, an angle, and the next side are equal (SAS), I can say with full confidence that those 2 are the exact same triangle with same sides, angles, etc. In fancy words they are said to be congruent

[final grotto]

Thank you. You yourself solved this task?

[wooden wave]

Uh yes?

GPT would've given the answer "6.3 million" in full confidence + explanation

Using GPT for answers to test problems feels like russian roulette

It either gived the exact answer of an answer differing by an order of mangnitude of 7

[topaz junco]

yea lol

like if you ask it "how long is one planck length" id expect it to say "4.4354e17" half the time lol

if its an equation wolfram alpha works pretty well

[wooden wave]

GPT is goated for science, got a perfect score on a bio quiz i didnt know sht on