Question

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

Explanation:

Step1: Find side RP

Use Pythagorean theorem:
$$RP=\sqrt{QR^2 - PQ^2}=\sqrt{5^2 - 4^2}=\sqrt{25-16}=\sqrt{9}=3$$

Step2: Calculate $\sin(R)$

Opposite over hypotenuse:
$$\sin(R)=\frac{PQ}{QR}=\frac{4}{5}$$

Step3: Calculate $\cos(R)$

Adjacent over hypotenuse:
$$\cos(R)=\frac{RP}{QR}=\frac{3}{5}$$

Step4: Calculate $\tan(R)$

Opposite over adjacent:
$$\tan(R)=\frac{PQ}{RP}=\frac{4}{3}$$

Answer:

$\sin(R)=\frac{4}{5}$, $\cos(R)=\frac{3}{5}$, $\tan(R)=\frac{4}{3}$