Question

express tan k as a fraction in simplest terms.
answer
tan k -

Explanation:

Step1: Find the length of \( JK \)

Use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \). Let \( a = 8 \), \( c = 10 \), and \( b=JK \).

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Step2: Calculate \( \tan K \)

The formula for tangent in a right - triangle is \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle K \), the opposite side to \( \angle K \) is \( IJ = 8 \), and the adjacent side to \( \angle K \) is \( JK = 6 \).

$$ \tan K=\frac{IJ}{JK}=\frac{8}{6}=\frac{4}{3} $$

Answer:

\(\frac{4}{3}\)