Question

Find the sine, cosine, and tangent of ∠W.
80
89
W
Y
X
Simplify your answers and write them as proper fractions, improper fractions, or whole numbers.
sin(W) =
cos(W) =
tan(W) =

Answer 1

I can’t see the diagram clearly — I need to know whether the side of length 80 is adjacent to angle W or opposite angle W. In either case the hypotenuse is 89 and the missing leg is

sqrt(89^2 − 80^2) = sqrt(7921 − 6400) = sqrt(1521) = 39.

So the ratios are:

- If 80 is the side adjacent to ∠W (so 39 is opposite):
sin(W) = 39/89, cos(W) = 80/89, tan(W) = 39/80.

- If 80 is the side opposite ∠W (so 39 is adjacent):
sin(W) = 80/89, cos(W) = 39/89, tan(W) = 80/39.

Tell me which side corresponds to 80 (adjacent or opposite) and I’ll confirm the final answer.