Question

In ΔWXY, the measure of ∠Y=90°, WY = 5, XW = 13, and YX = 12. What ratio represents the cosine of ∠W?

Answer 1

We can use the Pythagorean theorem to find the length of the third side of the triangle:

WX² + YX² = WY²

13² + 12² = WY²

169 + 144 = WY²

WY² = 313

WY = √313

Now we can use the definition of the cosine function to find cos(W):

cos(W) = adjacent/hypotenuse

The adjacent side to angle W is WX, which has length 13. The hypotenuse is WY, which we found to be √313. So:

cos(W) = 13/√313

To rationalize the denominator, we can multiply top and bottom by √313:

cos(W) = 13/√313 * √313/√313

cos(W) = 13√313/313

So the ratio that represents the cosine of angle W is 13√313/313.