Math mini-contest problem for Day 3 on D.Buzz for May 2021 😎

in D.Buzz β€’ 2 months ago

Math mini-contest problem for Day 3 on D.Buzz for May 2021 😎

Triangle ABC has C as the right angle. Fang recalls that the value of sin A has a numerator of 15. Manga remembered that the value of sin A is less than the value of cos A. What is the value of cos A?

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I think I don't fully get it...

     /|B
   /  |
A/____|C

sin(A) = BC/AB; BC=15 according to Fang, but AB still unknown.
cos(A) = AC/AB; we could substitute AB here, but AC still unknown
according to Manga: sin(A) < cos(A), so the angle at A is < pi/4.
Without knowing this information doesn't allow to calculate cos(A), we only know that it can only be between 0.707 and 1 from A < pi/4
I must be missing something...