To solve the problem, we need to determine the value of \( \cos A \) in the given right triangle \( \Delta ABC \). Let's go through the solution step by step.
Step 1: Identify the sides of the triangle
From the diagram:
- \( AC \) is the side opposite to angle \( B \), and its length is 5.
- \( BC \) is the side adjacent to angle \( A \), and its length is 12.
- \( AB \) is the hypotenuse, and its length is 13.
Step 2: Recall the definition of cosine
The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Mathematically:
\[
\cos A = \frac{\text{adjacent side}}{\text{hypotenuse}}
\]
Step 3: Identify the adjacent side and the hypotenuse for angle \( A \)
- The side adjacent to angle \( A \) is \( BC \), which has a length of 12.
- The hypotenuse is \( AB \), which has a length of 13.
Step 4: Substitute the values into the cosine formula
\[
\cos A = \frac{\text{adjacent side}}{\text{hypotenuse}} = \frac{BC}{AB} = \frac{12}{13}
\]
Step 5: Match the result with the given options
The options are:
1. \( \frac{5}{13} \)
2. \( \frac{12}{13} \)
3. \( \frac{5}{12} \)
4. \( \frac{13}{5} \)
The correct option is:
\[
\boxed{2}
\]
Final Answer:
\[
\boxed{\frac{12}{13}}
\]
Parent Tip: Review the logic above to help your child master the concept of sohcahtoa word problems worksheet.
