Find the exact value of cos(theta) if tan(theta)=-16/63 and theta is between 90 and 180 degrees

Question

I came up with -63/65. Is this correct? Thanks!

Answer 1

tan(theta) = -16/63

tangent = opposite side over adjacent side. adjacent side = -63, opposite side = 16

hypotenuse = square root of (adjacent side squared plus opposite side squared)

= sqr(63^2 + 16^2)

cosine of theta = adjacent side over hypotenuse = -63/sqr(63^2+16^2) = -63/65