Find the cosine ratio of angle Θ. Clue: Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces.

Question

Triangle ABC is shown. AB measures 15. BC measures 17. CA measures 8. The angle formed at point C is marked theta, and angle A is the right angle.

Answer for Blank 1:

Answer 1

To find the cosine ratio of angle Θ (which is the angle at point C in triangle ABC), we can use the definition of cosine in a right triangle.

In a triangle, the cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

1. Identify the sides relative to angle Θ at point C:

   • The side adjacent to Θ (which is angle C) is AB, which measures 15.
   • The hypotenuse is AC, which measures 17.

2. Now, we set up the cosine ratio: \[ \cos(Θ) = \text{Adjacent} / \text{Hypotenuse} = AB / AC = 15 / 17 \]

Thus, the answer for Blank 1 is: 15/17