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: Calculate side $TS$

Use Pythagorean theorem:
$$TS = \sqrt{TR^2 - SR^2} = \sqrt{68^2 - 32^2} = \sqrt{4624 - 1024} = \sqrt{3600} = 60$$

Step2: Find $\sin(R)$

Opposite over hypotenuse:
$$\sin(R) = \frac{TS}{TR} = \frac{60}{68} = \frac{15}{17}$$

Step3: Find $\cos(R)$

Adjacent over hypotenuse:
$$\cos(R) = \frac{SR}{TR} = \frac{32}{68} = \frac{8}{17}$$

Step4: Find $\tan(R)$

Opposite over adjacent:
$$\tan(R) = \frac{TS}{SR} = \frac{60}{32} = \frac{15}{8}$$

Answer:

$\sin(R)=\frac{15}{17}$, $\cos(R)=\frac{8}{17}$, $\tan(R)=\frac{15}{8}$