Question

find the cosine of $\angle d$. simplify your answer and write it as a proper fraction, improper fraction, or whole number. $\cos(d) = \square$

Explanation:

Step1: Confirm similar triangles

Triangles $IGH$ and $DEF$ are similar, so corresponding angles are congruent, meaning $\cos(\angle D) = \cos(\angle I)$.

Step2: Recall cosine definition

For right triangles, $\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$.

Step3: Identify sides for $\angle I$

Adjacent side to $\angle I$ is $IG = 39$, hypotenuse is $IH = 89$.

Step4: Calculate cosine value

$\cos(\angle D) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{39}{89}$

Answer:

$\frac{39}{89}$