Given 8 cot A = 15 for an acute angle A, find sin A and sec A.

Step 1. The ratio. $\cot A = \dfrac{15}{8}$, so adjacent $= 15k$ and opposite $= 8k$.

Step 2. The hypotenuse. $\sqrt{225k^2 + 64k^2} = \sqrt{289k^2} = 17k$.

Step 3. The ratios. $\sin A = \dfrac{8}{17} \approx 0.4706$ and $\sec A = \dfrac{17}{15} \approx 1.1333$.