A right triangle has acute angles C and D. If tan C=15/8 and cos D = 15/17, what are cot D and sin C?
To find cot D, we first need to find tan D. We know that tan D = 1 / tan C.
Given that tan C = 15/8, tan D = 1 / (15/8) = 8/15.
Now, cot D = 1 / tan D = 1 / (8/15) = 15/8.
Next, to find sin C, we can utilize the Pythagorean theorem, as sin C = sqrt(1 - cos^2 C).
Given that cos C = 15/17, sin C = sqrt(1 - (15/17)^2) = sqrt(1 - 225/289) = sqrt(64/289) = 8/17.
Therefore, cot D = 15/8 and sin C = 8/17.