Question

Find the sine, cosine, and tangent of ∠W.
80 is inbetween x and y
89 is inbetween w and x
W (which is at the peak of the triangle)
Y (stright down from W)
X (stright across from y)
Simplify your answers and write them as proper fractions, improper fractions, or whole numbers.
sin(W) =
cos(W) =
tan(W) =

Answer 1

Right triangle WYX with right angle at Y. Given WX (hypotenuse) = 89 and XY = 80, use Pythagoras to find WY:

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

For angle W:
sin(W) = opposite/hypotenuse = XY/WX = 80/89
cos(W) = adjacent/hypotenuse = WY/WX = 39/89
tan(W) = opposite/adjacent = XY/WY = 80/39

So:
sin(W) = 80/89
cos(W) = 39/89
tan(W) = 80/39