Question

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

Explanation:

Step1: Calculate hypotenuse $JK$

Use Pythagorean theorem:
$$JK = \sqrt{IJ^2 + IK^2} = \sqrt{5^2 + 12^2} = \sqrt{25+144} = \sqrt{169} = 13$$

Step2: Find $\sin(J)$

Opposite over hypotenuse:
$$\sin(J) = \frac{IK}{JK} = \frac{12}{13}$$

Step3: Find $\cos(J)$

Adjacent over hypotenuse:
$$\cos(J) = \frac{IJ}{JK} = \frac{5}{13}$$

Step4: Find $\tan(J)$

Opposite over adjacent:
$$\tan(J) = \frac{IK}{IJ} = \frac{12}{5}$$

Answer:

$\sin(J) = \frac{12}{13}$
$\cos(J) = \frac{5}{13}$
$\tan(J) = \frac{12}{5}$