Question

learn with an example or watch a video
find df.
write your answer as an integer or as a decimal rounded to the nearest tenth.
$df = \square$
in the right triangle $def$, $\angle d = 90^\circ$, side $ef = 9$, $\angle f = 42^\circ$

Explanation:

Step1: Identify trigonometric ratio

In right $\triangle DEF$, $\angle F=42^\circ$, hypotenuse $FE=9$, and $DF$ is the adjacent side to $\angle F$. Use cosine:
$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

Step2: Substitute known values

$\cos(42^\circ) = \frac{DF}{9}$

Step3: Solve for DF

Rearrange to isolate $DF$:
$DF = 9 \times \cos(42^\circ)$
Calculate $\cos(42^\circ) \approx 0.7431$, so:
$DF \approx 9 \times 0.7431$

Answer:

$6.7$