Question

Find the value of cos K rounded to the nearest hundredth, if necessary.
I
J
K
24
7
Answer
Attempt 2 out of 2

j has a 90 degree angle

Answer 1

To find the cosine of angle K in triangle IJK, where angle J is a right angle (90 degrees), we can use the definition of cosine in a right triangle.

In this triangle, we can define the sides:
- The side opposite angle K (let's call it side I) is 7.
- The side adjacent to angle K (let's call it side J) is 24.
- The hypotenuse (side K) can be calculated using the Pythagorean theorem.

### Step 1: Determine the length of the hypotenuse.

Using the Pythagorean theorem:

\[
\text{Hypotenuse}^2 = (\text{Opposite})^2 + (\text{Adjacent})^2
\]
\[
\text{Hypotenuse}^2 = 7^2 + 24^2
\]
\[
\text{Hypotenuse}^2 = 49 + 576
\]
\[
\text{Hypotenuse}^2 = 625
\]
\[
\text{Hypotenuse} = \sqrt{625} = 25
\]

### Step 2: Calculate \( \cos K \).

Now, use the cosine definition for angle K:
\[
\cos K = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{24}{25}
\]

### Step 3: Round to the nearest hundredth.

Calculating the decimal value:
\[
\frac{24}{25} = 0.96
\]

Thus, the value of \( \cos K \) rounded to the nearest hundredth is **0.96**.