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 length SR

Use Pythagorean theorem:
$$SR=\sqrt{QR^2 - QS^2}=\sqrt{40^2 - 32^2}=\sqrt{1600-1024}=\sqrt{576}=24$$

Step2: Define sides for ∠R

For $\angle R$:

• Opposite side: $QS=32$
• Adjacent side: $SR=24$
• Hypotenuse: $QR=40$

Step3: Calculate sin(R)

$\sin=\frac{\text{opposite}}{\text{hypotenuse}}$:
$$\sin(R)=\frac{32}{40}=\frac{4}{5}$$

Step4: Calculate cos(R)

$\cos=\frac{\text{adjacent}}{\text{hypotenuse}}$:
$$\cos(R)=\frac{24}{40}=\frac{3}{5}$$

Step5: Calculate tan(R)

$\tan=\frac{\text{opposite}}{\text{adjacent}}$:
$$\tan(R)=\frac{32}{24}=\frac{4}{3}$$

Answer:

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