Question

find the sine, cosine, and tangent of $\angle r$.
simplify your answers and write them as proper fractions, improper fractions, or whole numbers.
$\sin(r) = \square$
$\cos(r) = \square$
$\tan(r) = \square$

Explanation:

Step1: Find side QR via Pythagoras

$$QR = \sqrt{PR^2 - PQ^2} = \sqrt{89^2 - 80^2} = \sqrt{7921 - 6400} = \sqrt{1521} = 39$$

Step2: Calculate sin(R) (opp/hyp)

$$\sin(R) = \frac{PQ}{PR} = \frac{80}{89}$$

Step3: Calculate cos(R) (adj/hyp)

$$\cos(R) = \frac{QR}{PR} = \frac{39}{89}$$

Step4: Calculate tan(R) (opp/adj)

$$\tan(R) = \frac{PQ}{QR} = \frac{80}{39}$$

Answer:

$\sin(R) = \frac{80}{89}$
$\cos(R) = \frac{39}{89}$
$\tan(R) = \frac{80}{39}$