Question

find df.
write your answer as an integer or as a decimal rounded to the nearest tenth.
df =

Explanation:

Step1: Recall the cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 33^{\circ}\), the adjacent side to the angle \(33^{\circ}\) is \(DE = 3.9\), and the hypotenuse is \(DF\). So, \(\cos(33^{\circ})=\frac{DE}{DF}\).

Step2: Solve for \(DF\)

We can rewrite the formula as \(DF=\frac{DE}{\cos(33^{\circ})}\). Since \(DE = 3.9\) and \(\cos(33^{\circ})\approx0.8387\), then \(DF=\frac{3.9}{0.8387}\).

Step3: Calculate the value

\(DF=\frac{3.9}{0.8387}\approx4.6\)

Answer:

\(4.6\)