What is the exact value of the cos f?

cos(F) = 9/41

Step-by-step explanation:

The triangles are similar, so you know that ...

... cos(D) = cos(A) = 40/41.

From trig relations, you know ...

... cos(F) = sin(D)

and

... sin(D)² +cos(D)² = 1

So ...

... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)

... cos(F) = 9/41

The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.

From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know

... cos(F) = cos(C) = 9/41

it's both, now can you answer my most recent question?