Question

"Find sin B, cos B, tan B. Express each ratio as a fraction, sides: a = 16, b = 12, c =20

Answer 1

To find sin B, use the formula sin B = b/c. To find cos B, use the formula cos B = a/c. To find tan B, use the formula tan B = b/a.

Step-by-step explanation:

The correct answer is option Triangles, as the question is related to finding trigonometric ratios in a triangle.

1. To find sin B, we use the formula sin B = b/c, where b is the length of the side opposite angle B and c is the hypotenuse of the triangle. Substituting the given values, sin B = 12/20 = 0.6.
2. To find cos B, we use the formula cos B = a/c, where a is the length of the side adjacent to angle B. Substituting the given values, cos B = 16/20 = 0.8.
3. To find tan B, we use the formula tan B = b/a. Substituting the given values, tan B = 12/16 = 0.75.

The correct answer is that we can find sin B, cos B, and tan B using the given sides of the triangle (a = 16, b = 12, c = 20) and the fact that it’s a right-angled triangle as c, being the longest side, is the hypotenuse. By definition, sin B is opposite/ hypotenuse, so sin B = b/c = 12/20 = 3/5. Cos B is adjacent/hypotenuse, so cos B = a/c = 16/20 = 4/5. Finally, tan B is opposite/adjacent, so tan B = b/a = 12/16 = 3/4.