Question

Find the sine, cos, and tangent of ∠K.
32
40
K
J
I
Simplify your answers and write them as proper fractions, improper fractions, or whole numbers.
sin(K) =
cos(K) =
tan(K) =

Answer 1

I don’t have the diagram — could you confirm which side is which relative to ∠K (which length is opposite K, which is adjacent to K, and which is the hypotenuse)?

Two common interpretations and their answers:

1) If 32 is the side adjacent to ∠K and 40 is the hypotenuse (so the third side is 24, since 24-32-40 is a 3-4-5 triangle scaled by 8):
- sin(K) = 24/40 = 3/5
- cos(K) = 32/40 = 4/5
- tan(K) = 24/32 = 3/4

2) If 32 and 40 are the two legs (the right angle between them), then the hypotenuse = √(32^2 + 40^2) = 8√41. There are two subcases depending on which leg is opposite K:
- If opposite K = 32 and adjacent = 40:
- sin(K) = 32/(8√41) = 4/√41 = (4√41)/41
- cos(K) = 40/(8√41) = 5/√41 = (5√41)/41
- tan(K) = 32/40 = 4/5
- If opposite K = 40 and adjacent = 32:
- sin(K) = 40/(8√41) = 5/√41 = (5√41)/41
- cos(K) = 32/(8√41) = 4/√41 = (4√41)/41
- tan(K) = 40/32 = 5/4

Tell me which of these matches your diagram (or upload/describe the figure) and I’ll confirm.