Question

find the cosine of ∠r. simplify your answer and write it as a proper fraction, improper fraction, or whole number. cos(r) =
triangle with right angle at q, qr=8, qs=15, vertices r, q, s

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle R$, first find hypotenuse.
Using Pythagorean theorem: $c = \sqrt{a^2 + b^2}$, where $a = 8$, $b = 15$. So $c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$.

Step2: Identify adjacent side to $\angle R$

Adjacent side to $\angle R$ is $RQ = 8$, hypotenuse is $RS = 17$.
Thus, $\cos(R) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{8}{17}$.

Answer:

$\frac{8}{17}$