Question 820348
A drawing might help:<ol><li>Draw a right triangle.</li><li>Choose one of the acute angles. Let's call it angle A.</li><li>Label the sides so that tan(A) = 8/15. Since tan is opposite/adjacent, make the length of the side opposite angle A an 8 and make the length of the side adjacent to A a 15.</li></ol>Since we're looking for cos and since cos is adjacent/hypotenuse, we will need to find the hypotenuse. Use the Pythagorean Theorem:
{{{8^2 + 15^2 = h^2}}} (where "h" represents the length of the hypotenuse)
{{{64 + 225 = h^2}}}
{{{289 = h^2}}}
Square root of each side. (Since h can only be positive, we will use just the positive square root.)
{{{17 = h}}}<br>
Since tan(A) is positive, since we were told that sin(A) > 0 (positive) and since tan is sin/cos, cos must be positive. So:
{{{cos(A) = 8/17}}}