Questions: Find the value of cos θ. A. 5/12 B. 5/13 C. 12/13 D. 12/5

Find the value of cos θ. A. 5/12 B. 5/13 C. 12/13 D. 12/5
Transcript text: Find the value of $\cos \theta$. A. $\frac{5}{12}$ B. $\frac{5}{13}$ C. $\frac{12}{13}$ D. $\frac{12}{5}$
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Solution

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Solution Steps

Step 1: Identify the sides of the triangle

In the given right triangle, the sides are labeled as follows:

  • Hypotenuse (opposite the right angle): 13
  • Adjacent side to angle θ: 5
  • Opposite side to angle θ: 12
Step 2: Recall the cosine function definition

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: \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]

Step 3: Substitute the values into the cosine function

Using the given side lengths: \[ \cos(\theta) = \frac{5}{13} \]

Final Answer

\[ \cos(\theta) = \frac{5}{13} \]

The correct answer is B. \( \frac{5}{13} \).

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