A right triangle has acute angles C and D. If tan C=158 and cos D=1517, what are cot D and sin C?

Question

cot D=8/15 and sin C=8/17
cot D=8/15 and sin C=15/17
cot D=15/8 and sin C=15/17
cot D=15/8 and sin C=8/17

Answer 1

I labelled the triangle CDE, with E as the right angle.
All you have to do is recognize that your right-angled triangle
has sides EC = 8, DE = 15, and DC = 17
(you can check by using Pythagoras)

After that all you need to know are the definitions of the trig
functions in terms of opposite, adjacent, and hypotenuse, which
is usually taught at the start of the trig topic.

so cotD = adjacent/opposite = 15/8
and sinC = opposite/hyp = 15/17

Learning something like SOH CAH TOA would be of great help.