Select your answer If the hypotenuse has a length of 5 and the cosine of an angle equals 0.6, what is the length of the side opposite the angle? 1

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To determine the length of the side opposite the given angle in a right triangle, let's break down the problem step by step.

### **Given:**
- **Hypotenuse (c):** 5 units
- **Cosine of the angle (cosθ):** 0.6

### **Objective:**
Find the length of the side **opposite** the angle (let's denote it as **a**).

### **Understanding the Trigonometric Relationships:**
In a right triangle:
- **cosθ** = Adjacent side (**b**) / Hypotenuse (**c**)
- **sinθ** = Opposite side (**a**) / Hypotenuse (**c**)

Given **cosθ = 0.6**, we can first find the length of the adjacent side (**b**).

### **Step 1: Find the Adjacent Side (b)**
$$
\cosθ = \frac{b}{c} \
0.6 = \frac{b}{5} \
b = 0.6 \times 5 \
b = 3 \text{ units}
$$

### **Step 2: Use the Pythagorean Theorem to Find the Opposite Side (a)**
The Pythagorean theorem states that:
$$
a^2 + b^2 = c^2
$$
Plugging in the known values:
$$
a^2 + 3^2 = 5^2 \
a^2 + 9 = 25 \
a^2 = 25 - 9 \
a^2 = 16 \
a = \sqrt{16} \
a = 4 \text{ units}
$$

### **Conclusion:**
The length of the side opposite the given angle is **4 units**.
The length of the side opposite the angle is 4 units.

Select your answer If the hypotenuse has a length of 5 and the cosine of an angle equals 0.6, what is the length of the side opposite the angle? 1

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