Question

triangle 1: △def
cos(f) =
box
check
(diagram: right triangle △def with right angle at d, df = 5, de = 12, ef = 13)

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ for an acute angle $\theta$.

Step2: Identify sides for $\angle F$

For $\angle F$ in $\triangle DEF$ (right-angled at $D$), adjacent side to $\angle F$ is $DF = 5$, hypotenuse is $EF = 13$.

Step3: Calculate $\cos(F)$

Using the cosine definition: $\cos(F) = \frac{DF}{EF} = \frac{5}{13}$.

Answer:

$\frac{5}{13}$